170:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Sucesiones y series:@0.073089:0.043661:0.242349:0.043661:0.242349:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición  :@0.293264:0.254770:0.384306:0.254770:0.384306:0.237823:0.293264:0.237823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Una sucesión real ( ) se llama progresión geométrica si y solo si existe             :@0.377072:0.254770:0.930668:0.254770:0.930668:0.238336:0.377072:0.238336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.529686:0.254770:0.539000:0.254770:0.539000:0.238364:0.529686:0.238364:0.000000
n:@0.539193:0.257942:0.544730:0.257942:0.544730:0.248378:0.539193:0.248378:0.000000
d:@0.293269:0.271162:0.302527:0.271162:0.302527:0.254756:0.293269:0.254756:0.000000
     con   ≠ 0, tal que :@0.302546:0.271162:0.474006:0.271160:0.474006:0.254726:0.302546:0.254728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.306590:0.271558:0.321227:0.271558:0.321227:0.254706:0.306590:0.254706:0.000000
ℝ:@0.325275:0.271742:0.338565:0.271742:0.338565:0.254088:0.325275:0.254088:0.000000
d:@0.374552:0.271160:0.383810:0.271160:0.383810:0.254754:0.374552:0.254754:0.000000
u:@0.473932:0.271160:0.483246:0.271160:0.483246:0.254754:0.473932:0.254754:0.000000
n:@0.483267:0.274332:0.488804:0.274332:0.488804:0.264767:0.483267:0.264767:0.000000
+1:@0.488815:0.274332:0.500458:0.274332:0.500458:0.264751:0.488815:0.264751:0.000000:0.000000
 = :@0.500464:0.271160:0.519534:0.271160:0.519534:0.254726:0.500464:0.254726:0.000000:0.000000:0.000000
du:@0.519534:0.271160:0.538125:0.271160:0.538125:0.254754:0.519534:0.254754:0.000000:0.000000
n:@0.538155:0.274332:0.543693:0.274332:0.543693:0.264767:0.538155:0.264767:0.000000
,   :@0.543708:0.271160:0.559059:0.271160:0.559059:0.254726:0.543708:0.254726:0.000000:0.000000:0.000000:0.000000
∀:@0.559041:0.271742:0.571318:0.271742:0.571318:0.254088:0.559041:0.254088:0.000000
n:@0.571318:0.271160:0.580817:0.271160:0.580817:0.254754:0.571318:0.254754:0.000000
    , con:@0.580835:0.271160:0.653077:0.271160:0.653077:0.254726:0.580835:0.254726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.584893:0.271558:0.599529:0.271558:0.599529:0.254706:0.584893:0.254706:0.000000
ℕ:@0.603580:0.271742:0.617901:0.271742:0.617901:0.254088:0.603580:0.254088:0.000000
u:@0.653058:0.271160:0.662372:0.271160:0.662372:0.254754:0.653058:0.254754:0.000000
0:@0.662393:0.274332:0.667629:0.274332:0.667629:0.264751:0.662393:0.264751:0.000000
 :@0.667640:0.274332:0.669572:0.274332:0.669572:0.264767:0.667640:0.264767:0.000000
∈:@0.669581:0.271558:0.684218:0.271558:0.684218:0.254706:0.669581:0.254706:0.000000
   dado.:@0.684219:0.271160:0.746722:0.271160:0.746722:0.254726:0.684219:0.254726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.688268:0.271742:0.701558:0.271742:0.701558:0.254088:0.688268:0.254088:0.000000
De acuerdo con la definición de progresión geométrica, cada término se obtiene :@0.293267:0.298272:0.931036:0.298272:0.931036:0.281838:0.293267:0.281838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplicándole al término anterior la constante   Los  primeros términos se indican a :@0.293267:0.314664:0.930870:0.314664:0.930870:0.298230:0.293267:0.298230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d.:@0.645379:0.314664:0.657675:0.314664:0.657675:0.298258:0.645379:0.298258:0.000000:0.000000
k :@0.690812:0.314664:0.701728:0.314664:0.701728:0.298258:0.690812:0.298258:0.000000:0.000000
continuación: :@0.293267:0.331057:0.396734:0.331057:0.396734:0.314623:0.293267:0.314623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.293267:0.358169:0.302581:0.358169:0.302581:0.341763:0.293267:0.341763:0.000000
1:@0.302603:0.361334:0.307840:0.361334:0.307840:0.351753:0.302603:0.351753:0.000000
 = :@0.307847:0.358161:0.326917:0.358161:0.326917:0.341727:0.307847:0.341727:0.000000:0.000000:0.000000
du:@0.326917:0.358161:0.345508:0.358161:0.345508:0.341755:0.326917:0.341755:0.000000:0.000000
0:@0.345537:0.361334:0.350774:0.361334:0.350774:0.351753:0.345537:0.351753:0.000000
,       = :@0.350781:0.358161:0.407860:0.358161:0.407860:0.341727:0.350781:0.341727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.374214:0.358161:0.383528:0.358161:0.383528:0.341755:0.374214:0.341755:0.000000
2:@0.383548:0.361334:0.388785:0.361334:0.388785:0.351753:0.383548:0.351753:0.000000
du:@0.407860:0.358161:0.426452:0.358161:0.426452:0.341755:0.407860:0.341755:0.000000:0.000000
1:@0.426482:0.361334:0.431719:0.361334:0.431719:0.351753:0.426482:0.351753:0.000000
 =  (:@0.431726:0.358161:0.464951:0.358161:0.464951:0.341727:0.431726:0.341727:0.000000:0.000000:0.000000:0.000000:0.000000
d du:@0.450796:0.358161:0.483561:0.358161:0.483561:0.341755:0.450796:0.341755:0.000000:0.000000:0.000000:0.000000
0:@0.483591:0.361334:0.488828:0.361334:0.488828:0.351753:0.483591:0.351753:0.000000
) = :@0.488834:0.358161:0.512800:0.358161:0.512800:0.341727:0.488834:0.341727:0.000000:0.000000:0.000000:0.000000
u d ,:@0.512782:0.358161:0.545234:0.358161:0.545234:0.341755:0.512782:0.341755:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.522131:0.361334:0.527368:0.361334:0.527368:0.351753:0.522131:0.351753:0.000000
2:@0.536658:0.352097:0.541894:0.352097:0.541894:0.342516:0.536658:0.342516:0.000000
u:@0.293257:0.378131:0.302571:0.378131:0.302571:0.361725:0.293257:0.361725:0.000000
3:@0.302603:0.381298:0.307840:0.381298:0.307840:0.371717:0.302603:0.371717:0.000000
 = :@0.307847:0.378125:0.326917:0.378125:0.326917:0.361691:0.307847:0.361691:0.000000:0.000000:0.000000
du:@0.326917:0.378125:0.345508:0.378125:0.345508:0.361719:0.326917:0.361719:0.000000:0.000000
2:@0.345537:0.381298:0.350774:0.381298:0.350774:0.371717:0.345537:0.371717:0.000000
 = (:@0.350781:0.378125:0.383307:0.378125:0.383307:0.361691:0.350781:0.361691:0.000000:0.000000:0.000000:0.000000
 d u d:@0.365801:0.378125:0.407161:0.378125:0.407161:0.361719:0.365801:0.361719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.392658:0.381298:0.397895:0.381298:0.397895:0.371717:0.392658:0.371717:0.000000
2:@0.407186:0.372061:0.412423:0.372061:0.412423:0.362480:0.407186:0.362480:0.000000
) = :@0.412429:0.378125:0.436395:0.378125:0.436395:0.361691:0.412429:0.361691:0.000000:0.000000:0.000000:0.000000
u d ,   u:@0.436377:0.378125:0.488156:0.378125:0.488156:0.361719:0.436377:0.361719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.445726:0.381298:0.450963:0.381298:0.450963:0.371717:0.445726:0.371717:0.000000
3:@0.460254:0.372061:0.465491:0.372061:0.465491:0.362480:0.460254:0.362480:0.000000
4:@0.488211:0.381298:0.493448:0.381298:0.493448:0.371717:0.488211:0.371717:0.000000
 = :@0.493454:0.378125:0.512524:0.378125:0.512524:0.361691:0.493454:0.361691:0.000000:0.000000:0.000000
du:@0.512524:0.378125:0.531115:0.378125:0.531115:0.361719:0.512524:0.361719:0.000000:0.000000
3:@0.531145:0.381298:0.536382:0.381298:0.536382:0.371717:0.531145:0.371717:0.000000
 = (:@0.536390:0.378125:0.568916:0.378125:0.568916:0.361691:0.536390:0.361691:0.000000:0.000000:0.000000:0.000000
 d u d:@0.551410:0.378125:0.592768:0.378125:0.592768:0.361719:0.551410:0.361719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.578266:0.381298:0.583503:0.381298:0.583503:0.371717:0.578266:0.371717:0.000000
3:@0.592795:0.372061:0.598032:0.372061:0.598032:0.362480:0.592795:0.362480:0.000000
) = :@0.598037:0.378125:0.622004:0.378125:0.622004:0.361691:0.598037:0.361691:0.000000:0.000000:0.000000:0.000000
u d ,:@0.621985:0.378125:0.654437:0.378125:0.654437:0.361719:0.621985:0.361719:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.631335:0.381298:0.636571:0.381298:0.636571:0.371717:0.631335:0.371717:0.000000
4:@0.645861:0.372061:0.651098:0.372061:0.651098:0.362480:0.645861:0.362480:0.000000
∙:@0.293269:0.398678:0.302472:0.398678:0.302472:0.381024:0.293269:0.381024:0.000000
u:@0.293269:0.418066:0.302583:0.418066:0.302583:0.401659:0.293269:0.401659:0.000000
k:@0.302603:0.421224:0.307013:0.421224:0.307013:0.411659:0.302603:0.411659:0.000000
 = :@0.307029:0.418052:0.326099:0.418052:0.326099:0.401618:0.307029:0.401618:0.000000:0.000000:0.000000
du:@0.326099:0.418052:0.344690:0.418052:0.344690:0.401646:0.326099:0.401646:0.000000:0.000000
k–:@0.344720:0.421224:0.354475:0.421224:0.354475:0.411659:0.344720:0.411659:0.000000:0.000000
1:@0.354496:0.421224:0.359733:0.421224:0.359733:0.411643:0.354496:0.411643:0.000000
 = (:@0.359739:0.418052:0.392264:0.418052:0.392264:0.401618:0.359739:0.401618:0.000000:0.000000:0.000000:0.000000
 d u d:@0.374759:0.418052:0.416119:0.418052:0.416119:0.401646:0.374759:0.401646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.401615:0.421224:0.406852:0.421224:0.406852:0.411643:0.401615:0.411643:0.000000
k:@0.416144:0.411988:0.420554:0.411988:0.420554:0.402423:0.416144:0.402423:0.000000
–1:@0.420565:0.411988:0.431178:0.411988:0.431178:0.402407:0.420565:0.402407:0.000000:0.000000
) = :@0.431186:0.418052:0.455152:0.418052:0.455152:0.401618:0.431186:0.401618:0.000000:0.000000:0.000000:0.000000
u d ,   k :@0.455134:0.418052:0.507678:0.418052:0.507678:0.401646:0.455134:0.401646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.464483:0.421224:0.469720:0.421224:0.469720:0.411643:0.464483:0.411643:0.000000
k:@0.479009:0.411988:0.483420:0.411988:0.483420:0.402423:0.479009:0.402423:0.000000
 = 1, 2,...:@0.507733:0.418052:0.564961:0.418052:0.564961:0.401618:0.507733:0.401618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.564888:0.418052:0.568201:0.418052:0.568201:0.401646:0.564888:0.401646:0.000000
Así, el término general   de una progresión geométrica ( ) está definido como                   :@0.293252:0.446426:0.931030:0.446424:0.931030:0.429990:0.293252:0.429992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.476754:0.446426:0.486068:0.446426:0.486068:0.430020:0.476754:0.430020:0.000000
n:@0.486444:0.449596:0.491982:0.449596:0.491982:0.440031:0.486444:0.440031:0.000000
u:@0.748401:0.446424:0.757715:0.446424:0.757715:0.430017:0.748401:0.430017:0.000000
n:@0.758068:0.449596:0.763606:0.449596:0.763606:0.440031:0.758068:0.440031:0.000000
u:@0.293270:0.464078:0.302584:0.464078:0.302584:0.447672:0.293270:0.447672:0.000000
n:@0.302688:0.467246:0.308225:0.467246:0.308225:0.457682:0.302688:0.457682:0.000000
 = :@0.308291:0.464074:0.327894:0.464074:0.327894:0.447640:0.308291:0.447640:0.000000:0.000000:0.000000
u d n:@0.328428:0.464074:0.375442:0.464074:0.375442:0.447668:0.328428:0.447668:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.337863:0.467246:0.343099:0.467246:0.343099:0.457665:0.337863:0.457665:0.000000
n:@0.352537:0.458010:0.358074:0.458010:0.358074:0.448445:0.352537:0.448445:0.000000
,      . Además, el recorrido de la progresión geométrica ( ) es el conjunto     :@0.358139:0.464074:0.930888:0.464074:0.930888:0.447640:0.358139:0.447640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.380219:0.464472:0.394856:0.464472:0.394856:0.447621:0.380219:0.447621:0.000000
ℕ:@0.399644:0.464656:0.413965:0.464656:0.413965:0.447002:0.399644:0.447002:0.000000
u:@0.797554:0.464074:0.806868:0.464074:0.806868:0.447668:0.797554:0.447668:0.000000
n:@0.806980:0.467246:0.812517:0.467246:0.812517:0.457682:0.806980:0.457682:0.000000
{:@0.293259:0.481728:0.298136:0.481728:0.298136:0.465294:0.293259:0.465294:0.000000
u d  k:@0.298063:0.481728:0.346820:0.481724:0.346820:0.465318:0.298063:0.465322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.307400:0.484897:0.312637:0.484897:0.312637:0.475316:0.307400:0.475316:0.000000
 :@0.312648:0.484897:0.314580:0.484897:0.314580:0.475332:0.312648:0.475332:0.000000
k:@0.323783:0.475661:0.328193:0.475661:0.328193:0.466096:0.323783:0.466096:0.000000
 |     }.:@0.328155:0.481724:0.391913:0.481724:0.391913:0.465291:0.328155:0.465291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.350898:0.482123:0.365535:0.482123:0.365535:0.465271:0.350898:0.465271:0.000000
ℕ:@0.369585:0.482307:0.383906:0.482307:0.383906:0.464653:0.369585:0.464653:0.000000
Ejercicio 1:@0.293269:0.509086:0.369672:0.509086:0.369672:0.492417:0.293269:0.492417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea ( ) la sucesión definida como   = 3 × 4 ,      . De la definición de progresión :@0.293269:0.532621:0.931124:0.532624:0.931124:0.516191:0.293269:0.516187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.328979:0.532621:0.338293:0.532621:0.338293:0.516215:0.328979:0.516215:0.000000
n:@0.338418:0.535797:0.343956:0.535797:0.343956:0.526232:0.338418:0.526232:0.000000
u:@0.552605:0.532624:0.561919:0.532624:0.561919:0.516218:0.552605:0.516218:0.000000
n:@0.562048:0.535797:0.567585:0.535797:0.567585:0.526232:0.562048:0.526232:0.000000
–:@0.626652:0.526560:0.632018:0.526560:0.632018:0.516980:0.626652:0.516980:0.000000
n:@0.632050:0.526560:0.637588:0.526560:0.637588:0.516996:0.632050:0.516996:0.000000
n:@0.645577:0.532624:0.655075:0.532624:0.655075:0.516218:0.645577:0.516218:0.000000
∈:@0.660025:0.533023:0.674661:0.533023:0.674661:0.516171:0.660025:0.516171:0.000000
ℕ:@0.679623:0.533207:0.693944:0.533207:0.693944:0.515553:0.679623:0.515553:0.000000
geométrica, determinemos   y   :@0.293274:0.549017:0.541905:0.549014:0.541905:0.532580:0.293274:0.532583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.495367:0.549017:0.504681:0.549017:0.504681:0.532611:0.495367:0.532611:0.000000
0:@0.504701:0.552187:0.509659:0.552187:0.509659:0.542622:0.504701:0.542622:0.000000
d.:@0.525597:0.549014:0.537874:0.549014:0.537874:0.532608:0.525597:0.532608:0.000000:0.000000
Tenemos   = 3; por un lado,   = 3 × 4  =   , y por otro,   = :@0.293260:0.576126:0.739429:0.576125:0.739429:0.559691:0.293260:0.559693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.363447:0.576126:0.372761:0.576126:0.372761:0.559720:0.363447:0.559720:0.000000
0:@0.372790:0.579297:0.377747:0.579297:0.377747:0.569733:0.372790:0.569733:0.000000
u:@0.503538:0.576125:0.512852:0.576125:0.512852:0.559719:0.503538:0.559719:0.000000
1:@0.512874:0.579297:0.518111:0.579297:0.518111:0.569717:0.512874:0.569717:0.000000
–1:@0.573504:0.570061:0.584064:0.570061:0.584064:0.560480:0.573504:0.560480:0.000000:0.000000
3:@0.605429:0.569549:0.614412:0.569549:0.614412:0.553115:0.605429:0.553115:0.000000
4:@0.605429:0.585941:0.614412:0.585941:0.614412:0.569508:0.605429:0.569508:0.000000
u:@0.705951:0.576123:0.715265:0.576123:0.715265:0.559717:0.705951:0.559717:0.000000
1:@0.715298:0.579297:0.720535:0.579297:0.720535:0.569717:0.715298:0.569717:0.000000
du:@0.739337:0.576125:0.757928:0.576125:0.757928:0.559719:0.739337:0.559719:0.000000:0.000000
0:@0.757958:0.579297:0.763195:0.579297:0.763195:0.569717:0.757958:0.569717:0.000000
 = 3  =    .:@0.763202:0.576125:0.844229:0.576131:0.844229:0.559698:0.763202:0.559691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.790887:0.576125:0.800146:0.576125:0.800146:0.559719:0.790887:0.559719:0.000000
3:@0.825546:0.568657:0.834529:0.568657:0.834529:0.552223:0.825546:0.552223:0.000000
4:@0.825546:0.585049:0.834529:0.585049:0.834529:0.568615:0.825546:0.568615:0.000000
Luego,   =   .:@0.293264:0.603244:0.394045:0.603243:0.394045:0.586809:0.293264:0.586810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.346037:0.603244:0.355296:0.603244:0.355296:0.586838:0.346037:0.586838:0.000000
1:@0.376282:0.595768:0.385265:0.595768:0.385265:0.579334:0.376282:0.579334:0.000000
4:@0.376282:0.612160:0.385265:0.612160:0.385265:0.595726:0.376282:0.595726:0.000000
Resulta   = :@0.293265:0.630355:0.383021:0.630347:0.383021:0.613913:0.293265:0.613921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.349555:0.630355:0.358869:0.630355:0.358869:0.613949:0.349555:0.613949:0.000000
2:@0.358892:0.633520:0.364129:0.633520:0.364129:0.623939:0.358892:0.623939:0.000000
du:@0.382929:0.630347:0.401520:0.630347:0.401520:0.613941:0.382929:0.613941:0.000000:0.000000
1:@0.401550:0.633520:0.406787:0.633520:0.406787:0.623939:0.401550:0.623939:0.000000
 =    ×    = :@0.406794:0.630347:0.499467:0.630355:0.499467:0.613921:0.406794:0.613913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.428209:0.622879:0.437192:0.622879:0.437192:0.606445:0.428209:0.606445:0.000000
4:@0.428209:0.639271:0.437192:0.639271:0.437192:0.622837:0.428209:0.622837:0.000000
3:@0.465100:0.621091:0.474083:0.621091:0.474083:0.604657:0.465100:0.604657:0.000000
4:@0.465100:0.637483:0.474083:0.637483:0.474083:0.621049:0.465100:0.621049:0.000000
3:@0.504365:0.621545:0.513347:0.621545:0.513347:0.605111:0.504365:0.605111:0.000000
4:@0.501788:0.637937:0.510770:0.637937:0.510770:0.621503:0.501788:0.621503:0.000000
2:@0.510688:0.631871:0.515925:0.631871:0.515925:0.622290:0.510688:0.622290:0.000000
  ,    = :@0.518262:0.630347:0.570656:0.630347:0.570656:0.613913:0.518262:0.613913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.537185:0.630347:0.546499:0.630347:0.546499:0.613941:0.537185:0.613941:0.000000
3:@0.546526:0.633520:0.551762:0.633520:0.551762:0.623939:0.546526:0.623939:0.000000
du:@0.570564:0.630347:0.589155:0.630347:0.589155:0.613941:0.570564:0.613941:0.000000:0.000000
2:@0.589185:0.633520:0.594422:0.633520:0.594422:0.623939:0.589185:0.623939:0.000000
 =     × :@0.594430:0.630347:0.654161:0.630349:0.654161:0.613915:0.594430:0.613913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.619795:0.623331:0.628778:0.623331:0.628778:0.606897:0.619795:0.606897:0.000000
4:@0.619795:0.639723:0.628778:0.639723:0.628778:0.623290:0.619795:0.623290:0.000000
3:@0.659057:0.622879:0.668040:0.622879:0.668040:0.606445:0.659057:0.606445:0.000000
4:@0.656480:0.639271:0.665463:0.639271:0.665463:0.622837:0.656480:0.622837:0.000000
2:@0.665381:0.633205:0.670618:0.633205:0.670618:0.623623:0.665381:0.623623:0.000000
  =  :@0.672955:0.630347:0.699756:0.630347:0.699756:0.613913:0.672955:0.613913:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.704644:0.621985:0.713627:0.621985:0.713627:0.605551:0.704644:0.605551:0.000000
4:@0.702067:0.638377:0.711050:0.638377:0.711050:0.621943:0.702067:0.621943:0.000000
3:@0.710968:0.632311:0.716204:0.632311:0.716204:0.622730:0.710968:0.622730:0.000000
 .:@0.718541:0.630347:0.725702:0.630347:0.725702:0.613913:0.718541:0.613913:0.000000:0.000000
El recorrido de esta sucesión está definido como el conjunto: :@0.293260:0.657460:0.738092:0.657460:0.738092:0.641026:0.293260:0.641026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.620494:0.677020:0.629477:0.677020:0.629477:0.660586:0.620494:0.660586:0.000000
4 4:@0.620494:0.693412:0.655006:0.693412:0.655006:0.676978:0.620494:0.676978:0.000000:0.000000:0.000000
3:@0.648601:0.677020:0.657583:0.677020:0.657583:0.660586:0.648601:0.660586:0.000000
2:@0.654924:0.687346:0.660161:0.687346:0.660161:0.677765:0.654924:0.677765:0.000000
3:@0.681382:0.677020:0.690365:0.677020:0.690365:0.660586:0.681382:0.660586:0.000000
4:@0.678805:0.693412:0.687788:0.693412:0.687788:0.676978:0.678805:0.676978:0.000000
3:@0.687706:0.687346:0.692943:0.687346:0.692943:0.677765:0.687706:0.677765:0.000000
3:@0.488297:0.677020:0.497279:0.677020:0.497279:0.660586:0.488297:0.660586:0.000000
4:@0.485572:0.693412:0.494555:0.693412:0.494555:0.676978:0.485572:0.676978:0.000000
n:@0.494472:0.687346:0.500009:0.687346:0.500009:0.677781:0.494472:0.677781:0.000000
     n:@0.499657:0.685533:0.530272:0.685533:0.530272:0.669127:0.499657:0.669127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 |        =   3,      ,       ,       , ...   .:@0.509674:0.685533:0.731000:0.685533:0.731000:0.669099:0.509674:0.669099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.534352:0.685931:0.548988:0.685931:0.548988:0.669079:0.534352:0.669079:0.000000
ℕ:@0.553038:0.686115:0.567359:0.686115:0.567359:0.668461:0.553038:0.668461:0.000000
Se tiene :@0.293275:0.721562:0.357953:0.721562:0.357953:0.705128:0.293275:0.705128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.358952:0.721562:0.368266:0.721562:0.368266:0.705156:0.358952:0.705156:0.000000
n:@0.368430:0.724731:0.373968:0.724731:0.373968:0.715166:0.368430:0.715166:0.000000
+1:@0.374075:0.724731:0.385826:0.724731:0.385826:0.715150:0.374075:0.715150:0.000000:0.000000
 – :@0.385934:0.721558:0.404341:0.721558:0.404341:0.705125:0.385934:0.705125:0.000000:0.000000:0.000000
u:@0.405372:0.721558:0.414686:0.721558:0.414686:0.705152:0.405372:0.705152:0.000000
n :@0.414860:0.724731:0.422437:0.724731:0.422437:0.715166:0.414860:0.715166:0.000000:0.000000
 =  :@0.422981:0.721558:0.448217:0.721558:0.448217:0.705125:0.422981:0.705125:0.000000:0.000000:0.000000:0.000000
1:@0.481503:0.715875:0.490486:0.715875:0.490486:0.699441:0.481503:0.699441:0.000000
4:@0.481503:0.732267:0.490486:0.732267:0.490486:0.715833:0.481503:0.715833:0.000000
3:@0.454240:0.715875:0.463223:0.715875:0.463223:0.699441:0.454240:0.699441:0.000000
4:@0.451516:0.732267:0.460498:0.732267:0.460498:0.715833:0.451516:0.715833:0.000000
n:@0.460415:0.726201:0.465952:0.726201:0.465952:0.716636:0.460415:0.716636:0.000000
 – 1  < 0,   :@0.496679:0.723025:0.575383:0.721558:0.575383:0.705125:0.496679:0.706591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.576396:0.722141:0.588673:0.722141:0.588673:0.704487:0.576396:0.704487:0.000000
n:@0.588876:0.721558:0.598374:0.721558:0.598374:0.705152:0.588876:0.705152:0.000000
     que muestra que ( ) es una sucesión :@0.598558:0.721558:0.931016:0.721558:0.931016:0.705125:0.598558:0.705125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.603722:0.721957:0.618358:0.721957:0.618358:0.705105:0.603722:0.705105:0.000000
ℕ:@0.623714:0.722141:0.638035:0.722141:0.638035:0.704487:0.623714:0.704487:0.000000
u:@0.782403:0.721558:0.791717:0.721558:0.791717:0.705152:0.782403:0.705152:0.000000
n:@0.791901:0.724731:0.797438:0.724731:0.797438:0.715166:0.791901:0.715166:0.000000
estrictamente decreciente.:@0.293259:0.744247:0.486805:0.744247:0.486805:0.727813:0.293259:0.727813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio 2:@0.293259:0.771609:0.369661:0.771609:0.369661:0.754939:0.293259:0.754939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los cuatro primeros términos de una progresión geométrica son 3, 6, 12, 24. :@0.293259:0.795143:0.931031:0.795143:0.931031:0.778709:0.293259:0.778709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determinemos el término general de la progresión geométrica. Ponemos   = 3,   = 6. :@0.293259:0.811535:0.930935:0.811542:0.930935:0.795108:0.293259:0.795101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.830898:0.811535:0.840212:0.811535:0.840212:0.795129:0.830898:0.795129:0.000000
0:@0.840248:0.814714:0.845485:0.814714:0.845485:0.805133:0.840248:0.805133:0.000000
u:@0.880964:0.811542:0.890278:0.811542:0.890278:0.795135:0.880964:0.795135:0.000000
1:@0.890303:0.814714:0.895540:0.814714:0.895540:0.805133:0.890303:0.805133:0.000000
Luego, :@0.293260:0.827934:0.346222:0.827934:0.346222:0.811500:0.293260:0.811500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.293260:0.855046:0.302574:0.855046:0.302574:0.838640:0.293260:0.838640:0.000000
1:@0.302603:0.858215:0.307840:0.858215:0.307840:0.848634:0.302603:0.848634:0.000000
 = :@0.307845:0.855042:0.326915:0.855042:0.326915:0.838609:0.307845:0.838609:0.000000:0.000000:0.000000
u d:@0.326915:0.855042:0.350756:0.855042:0.350756:0.838636:0.326915:0.838636:0.000000:0.000000:0.000000
0:@0.336253:0.858215:0.341490:0.858215:0.341490:0.848634:0.336253:0.848634:0.000000
 :@0.350774:0.855042:0.354806:0.855042:0.354806:0.838609:0.350774:0.838609:0.000000
⇔:@0.354824:0.854626:0.374004:0.854626:0.374004:0.837638:0.354824:0.837638:0.000000
 6 = 3  :@0.374004:0.855042:0.428416:0.855042:0.428416:0.838609:0.374004:0.838609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.415108:0.855042:0.424367:0.855042:0.424367:0.838636:0.415108:0.838636:0.000000
⇔:@0.428435:0.854626:0.447615:0.854626:0.447615:0.837638:0.428435:0.837638:0.000000
   = 2   Por lo tanto, :@0.447615:0.855042:0.591282:0.855042:0.591282:0.838609:0.447615:0.838609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.451665:0.855042:0.460923:0.855042:0.460923:0.838636:0.451665:0.838636:0.000000
.:@0.488995:0.855042:0.492326:0.855042:0.492326:0.838636:0.488995:0.838636:0.000000
u:@0.293252:0.875013:0.302566:0.875013:0.302566:0.858606:0.293252:0.858606:0.000000
2:@0.302603:0.878177:0.307840:0.878177:0.307840:0.868596:0.302603:0.868596:0.000000
 = :@0.307845:0.875005:0.326915:0.875005:0.326915:0.858571:0.307845:0.858571:0.000000:0.000000:0.000000
u d:@0.326915:0.875005:0.350754:0.875005:0.350754:0.858599:0.326915:0.858599:0.000000:0.000000:0.000000
1:@0.336253:0.878177:0.341490:0.878177:0.341490:0.868596:0.336253:0.868596:0.000000
 = 6 × 2 12,:@0.350773:0.875005:0.445589:0.875005:0.445589:0.858571:0.350773:0.858571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.406897:0.875005:0.424531:0.875005:0.424531:0.858599:0.406897:0.858599:0.000000:0.000000:0.000000
u:@0.293250:0.894975:0.302564:0.894975:0.302564:0.878569:0.293250:0.878569:0.000000
n:@0.302603:0.898142:0.308140:0.898142:0.308140:0.888577:0.302603:0.888577:0.000000
+1:@0.308151:0.898142:0.319794:0.898142:0.319794:0.888560:0.308151:0.888560:0.000000:0.000000
 = :@0.319802:0.894969:0.338872:0.894969:0.338872:0.878535:0.319802:0.878535:0.000000:0.000000:0.000000
u d:@0.338872:0.894969:0.363020:0.894969:0.363020:0.878563:0.338872:0.878563:0.000000:0.000000:0.000000
n:@0.348209:0.898142:0.353747:0.898142:0.353747:0.888577:0.348209:0.888577:0.000000
 = :@0.363039:0.894969:0.382109:0.894969:0.382109:0.878535:0.363039:0.878535:0.000000:0.000000:0.000000
u d:@0.382109:0.894969:0.405954:0.894969:0.405954:0.878563:0.382109:0.878563:0.000000:0.000000:0.000000
0:@0.391453:0.898142:0.396690:0.898142:0.396690:0.888560:0.391453:0.888560:0.000000
n:@0.405981:0.888905:0.411519:0.888905:0.411519:0.879340:0.405981:0.879340:0.000000
+1:@0.411529:0.888905:0.423173:0.888905:0.423173:0.879324:0.411529:0.879324:0.000000:0.000000
 = 3 × 2 ,      .:@0.423180:0.894969:0.553350:0.894969:0.553350:0.878535:0.423180:0.878535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.479302:0.888905:0.484840:0.888905:0.484840:0.879340:0.479302:0.879340:0.000000
+1:@0.484850:0.888905:0.496494:0.888905:0.496494:0.879324:0.484850:0.879324:0.000000:0.000000
n:@0.503570:0.894969:0.513068:0.894969:0.513068:0.878563:0.503570:0.878563:0.000000
∈:@0.517141:0.895367:0.531777:0.895367:0.531777:0.878515:0.517141:0.878515:0.000000
ℕ:@0.535826:0.895551:0.550147:0.895551:0.550147:0.877897:0.535826:0.877897:0.000000
Como :@0.293274:0.922081:0.341906:0.922081:0.341906:0.905647:0.293274:0.905647:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.341390:0.922081:0.350704:0.922081:0.350704:0.905675:0.341390:0.905675:0.000000
n:@0.350692:0.925252:0.356230:0.925252:0.356230:0.915688:0.350692:0.915688:0.000000
+1:@0.356230:0.925252:0.367852:0.925252:0.367852:0.915671:0.356230:0.915671:0.000000:0.000000
 –   = 3 × 2  – 3 × 2  = 3 × 2  > 0,   :@0.367841:0.922080:0.628078:0.922080:0.628078:0.905646:0.367841:0.905646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.384242:0.922080:0.393556:0.922080:0.393556:0.905674:0.384242:0.905674:0.000000
n:@0.393560:0.925252:0.399097:0.925252:0.399097:0.915688:0.393560:0.915688:0.000000
n:@0.453089:0.916016:0.458626:0.916016:0.458626:0.906451:0.453089:0.906451:0.000000
+1:@0.458626:0.916016:0.470248:0.916016:0.470248:0.906435:0.458626:0.906435:0.000000:0.000000
n:@0.522277:0.916016:0.527814:0.916016:0.527814:0.906451:0.522277:0.906451:0.000000
n:@0.581622:0.916016:0.587159:0.916016:0.587159:0.906451:0.581622:0.906451:0.000000
∀:@0.627563:0.922662:0.639840:0.922662:0.639840:0.905008:0.627563:0.905008:0.000000
n:@0.639804:0.922080:0.649302:0.922080:0.649302:0.905674:0.639804:0.905674:0.000000
    , se sigue que ( ) es una sucesión :@0.649302:0.922080:0.930946:0.922080:0.930946:0.905646:0.649302:0.905646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.652918:0.922478:0.667554:0.922478:0.667554:0.905627:0.652918:0.905627:0.000000
ℕ:@0.671129:0.922662:0.685450:0.922662:0.685450:0.905008:0.671129:0.905008:0.000000
u:@0.790132:0.922080:0.799446:0.922080:0.799446:0.905674:0.790132:0.905674:0.000000
n:@0.799448:0.925252:0.804985:0.925252:0.804985:0.915688:0.799448:0.915688:0.000000
estrictamente creciente. El recorrido de esta sucesión es el conjunto {3 × 2 |     }. :@0.293264:0.938472:0.904619:0.938470:0.904619:0.922036:0.293264:0.922038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.829955:0.932406:0.835493:0.932406:0.835493:0.922841:0.829955:0.922841:0.000000
   n:@0.835508:0.938470:0.855498:0.938470:0.855498:0.922064:0.835508:0.922064:0.000000:0.000000:0.000000:0.000000
∈:@0.859573:0.938868:0.874209:0.938868:0.874209:0.922016:0.859573:0.922016:0.000000
ℕ:@0.878259:0.939052:0.892580:0.939052:0.892580:0.921398:0.878259:0.921398:0.000000
Tema 3. Progresiones geométricas:@0.073089:0.098522:0.580520:0.098522:0.580520:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Un tanque tiene una fuga que reduce la cantidad de agua en un 10 % cada día. Si el :@0.294207:0.164216:0.902913:0.164216:0.902913:0.147782:0.294207:0.147782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tanque originalmente tiene 1000 litros, ¿cuánta agua quedará después de 7 días?:@0.294207:0.180858:0.880443:0.180858:0.880443:0.164424:0.294207:0.164424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Modela la situación con una progresión geométrica donde a1=1000 y r = 0,9, y :@0.294207:0.201077:0.902486:0.201077:0.902486:0.184644:0.294207:0.184644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calcula el séptimo término.:@0.294207:0.217719:0.489784:0.217719:0.489784:0.201286:0.294207:0.201286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302129:0.139844:0.424604:0.139844:0.424604:0.124438:0.302129:0.124438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinaria :@0.078581:0.259885:0.201990:0.259885:0.201990:0.244479:0.078581:0.244479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Según una leyenda, un an-:@0.079392:0.317127:0.252414:0.317127:0.252414:0.302934:0.079392:0.302934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiguo sabio inventó el aje-:@0.079390:0.331499:0.247757:0.331499:0.247757:0.317306:0.079390:0.317306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
drez y presentó el juego a :@0.079390:0.345872:0.249917:0.345872:0.249917:0.331679:0.079390:0.331679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un rey. El rey, impresionado, :@0.079390:0.360244:0.262334:0.360244:0.262334:0.346051:0.079390:0.346051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
le ofreció una recompensa :@0.079390:0.374617:0.255053:0.374617:0.255053:0.360424:0.079390:0.360424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a su elección. El sabio pidió :@0.079390:0.388989:0.259314:0.388989:0.259314:0.374796:0.079390:0.374796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un grano de trigo por la :@0.079390:0.403361:0.237312:0.403361:0.237312:0.389169:0.079390:0.389169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
primera casilla del tablero, :@0.079390:0.417734:0.251826:0.417734:0.251826:0.403541:0.079390:0.403541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos granos por la segunda :@0.079390:0.432106:0.254608:0.432106:0.254608:0.417914:0.079390:0.417914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
casilla, cuatro granos por la :@0.079390:0.446479:0.258010:0.446479:0.258010:0.432286:0.079390:0.432286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tercera, y así sucesivamen-:@0.079390:0.460851:0.250761:0.460851:0.250761:0.446659:0.079390:0.446659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
te, duplicando la cantidad :@0.079390:0.475224:0.251079:0.475224:0.251079:0.461031:0.079390:0.461031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de granos en cada casilla.:@0.079390:0.489596:0.243671:0.489596:0.243671:0.475404:0.079390:0.475404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Progresión geométrica::@0.079390:0.511119:0.236549:0.511119:0.236549:0.496723:0.079390:0.496723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Primer término ( ): :@0.079392:0.525489:0.233330:0.525489:0.233330:0.511092:0.079392:0.511092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.208693:0.525489:0.216991:0.525489:0.216991:0.511080:0.208693:0.511080:0.000000
1:@0.217148:0.528229:0.221902:0.528229:0.221902:0.519836:0.217148:0.519836:0.000000
1 grano en la primera :@0.098363:0.539861:0.240468:0.539861:0.240468:0.525668:0.098363:0.525668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
casilla.:@0.098363:0.554234:0.139760:0.554234:0.139760:0.540041:0.098363:0.540041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Razón ( ): :@0.079392:0.568606:0.164721:0.568606:0.164721:0.554210:0.079392:0.554210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.148013:0.568606:0.153069:0.568606:0.153069:0.554198:0.148013:0.554198:0.000000
2, porque el :@0.164880:0.568606:0.245193:0.568606:0.245193:0.554413:0.164880:0.554413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número de granos se :@0.098366:0.582979:0.239152:0.582979:0.239152:0.568786:0.098366:0.568786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
duplica en cada casilla.:@0.098366:0.597351:0.246019:0.597351:0.246019:0.583158:0.098366:0.583158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Fórmula del término :@0.079392:0.611724:0.239613:0.611724:0.239613:0.597327:0.079392:0.597327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n-ésimo (a ):  :@0.098366:0.626096:0.189717:0.626096:0.189717:0.611700:0.098366:0.611700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.169458:0.628836:0.174602:0.628836:0.174602:0.620443:0.169458:0.620443:0.000000
an:@0.098372:0.640469:0.114730:0.640469:0.114730:0.626300:0.098372:0.626300:0.000000:0.000000
 = :@0.114889:0.640469:0.131644:0.640469:0.131644:0.626276:0.114889:0.626276:0.000000:0.000000:0.000000
a:@0.131803:0.640469:0.139800:0.640469:0.139800:0.626300:0.131803:0.626300:0.000000
1:@0.139953:0.643209:0.144476:0.643209:0.144476:0.634935:0.139953:0.634935:0.000000
∙:@0.144568:0.640972:0.149862:0.640972:0.149862:0.625725:0.144568:0.625725:0.000000
 r:@0.150021:0.640469:0.158351:0.640469:0.158351:0.626276:0.150021:0.626276:0.000000:0.000000
n:@0.158510:0.640469:0.166713:0.640469:0.166713:0.626300:0.158510:0.626300:0.000000
-1:@0.166871:0.635232:0.174248:0.635232:0.174248:0.626958:0.166871:0.626958:0.000000:0.000000
, que en este :@0.174341:0.640469:0.260106:0.640469:0.260106:0.626276:0.174341:0.626276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
caso sería  :@0.098368:0.654841:0.168236:0.654841:0.168236:0.640648:0.098368:0.640648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
an:@0.098368:0.669669:0.114727:0.669669:0.114727:0.655500:0.098368:0.655500:0.000000:0.000000
 = 1 2:@0.114886:0.669669:0.152927:0.669669:0.152927:0.655476:0.114886:0.655476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∙:@0.139717:0.670172:0.145011:0.670172:0.145011:0.654925:0.139717:0.654925:0.000000
n:@0.153086:0.669669:0.161289:0.669669:0.161289:0.655500:0.153086:0.655500:0.000000
-1:@0.161446:0.664431:0.168823:0.664431:0.168823:0.656157:0.161446:0.656157:0.000000:0.000000
.:@0.168916:0.669667:0.171682:0.669667:0.171682:0.655475:0.168916:0.655475:0.000000
¿Cuál es el número total :@0.079399:0.787821:0.238655:0.787821:0.238655:0.773628:0.079399:0.773628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de granos de trigo que se :@0.079399:0.802194:0.248704:0.802194:0.248704:0.788001:0.079399:0.788001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
acumulan en un tablero de :@0.079399:0.816566:0.258449:0.816566:0.258449:0.802373:0.079399:0.802373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ajedrez, hasta llegar a la 64ª :@0.079399:0.830939:0.260579:0.830939:0.260579:0.816746:0.079399:0.816746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
casilla? :@0.079399:0.845311:0.127567:0.845311:0.127567:0.831118:0.079399:0.831118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Con cuáles disciplinas del :@0.079399:0.866834:0.254395:0.866834:0.254395:0.852641:0.079399:0.852641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
saber puedes relacionar :@0.079399:0.881207:0.236989:0.881207:0.236989:0.867014:0.079399:0.867014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esta leyenda de progresio-:@0.079399:0.895579:0.251231:0.895579:0.251231:0.881386:0.079399:0.881386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes geométricas?:@0.079399:0.910407:0.192301:0.910407:0.192301:0.896214:0.079399:0.896214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 3 (Ev. 2) Determina y utiliza la expresión general de una sucesión para calcular cualquier valor de la misma y para compararla con otras sucesiones.:@0.082824:0.965315:0.826116:0.965315:0.826116:0.953363:0.082824:0.953363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
EC. Reconoce progresiones geométricas y sus propiedades. EC. Deduce fórmulas para un término cualquiera, así como la suma de los términos de una progresión geométrica.:@0.082824:0.977418:0.943921:0.977418:0.943921:0.965466:0.082824:0.965466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000