124:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000 :@0.404236:0.110451:0.408378:0.110451:0.408378:0.093953:0.404236:0.093953:0.000000 Calculamos la suma de los primeros términos::@0.427971:0.110451:0.766614:0.110451:0.766614:0.093953:0.427971:0.093953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.618870:0.110566:0.628233:0.110566:0.628233:0.094098:0.618870:0.094098:0.000000 S:@0.571266:0.135045:0.579145:0.135045:0.579145:0.118577:0.571266:0.118577:0.000000 n:@0.579076:0.138275:0.584535:0.138275:0.584535:0.128673:0.579076:0.128673:0.000000 = + + … + :@0.584536:0.134929:0.700726:0.134929:0.700726:0.118431:0.584536:0.118431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 g:@0.603627:0.135045:0.611064:0.135045:0.611064:0.118576:0.603627:0.118576:0.000000 0:@0.611063:0.138207:0.616016:0.138207:0.616016:0.128589:0.611063:0.128589:0.000000 g:@0.635107:0.135045:0.642543:0.135045:0.642543:0.118576:0.635107:0.118576:0.000000 1:@0.642542:0.138207:0.647496:0.138207:0.647496:0.128589:0.642542:0.128589:0.000000 g:@0.700726:0.135045:0.708162:0.135045:0.708162:0.118576:0.700726:0.118576:0.000000 n:@0.708200:0.138275:0.713659:0.138275:0.713659:0.128673:0.708200:0.128673:0.000000 –1:@0.713659:0.138207:0.724733:0.138207:0.724733:0.128589:0.713659:0.128589:0.000000:0.000000 :@0.404236:0.180793:0.408378:0.180793:0.408378:0.164295:0.404236:0.164295:0.000000 = + + … + = = – 1, .:@0.427971:0.180793:0.891762:0.180793:0.891762:0.164295:0.427971:0.164295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.841423:0.180909:0.850786:0.180909:0.850786:0.164440:0.841423:0.164440:0.000000 :@0.855040:0.180274:0.869692:0.180274:0.869692:0.166901:0.855040:0.166901:0.000000 N:@0.873922:0.179824:0.888911:0.179824:0.888911:0.166377:0.873922:0.166377:0.000000 :@0.404235:0.198144:0.408377:0.198144:0.408377:0.181646:0.404235:0.181646:0.000000 2.:@0.404235:0.226266:0.416507:0.226266:0.416507:0.209552:0.404235:0.209552:0.000000:0.000000 Considera la fracción periódica = 3,525252… Se trata de:@0.416507:0.226050:0.837274:0.226050:0.837274:0.209552:0.416507:0.209552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.651443:0.226165:0.660652:0.226165:0.660652:0.209696:0.651443:0.209696:0.000000 :@0.404235:0.250529:0.408377:0.250529:0.408377:0.234031:0.404235:0.234031:0.000000 determinar un número racional = con , :@0.427970:0.250529:0.785021:0.250534:0.785021:0.234037:0.427970:0.234031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 r:@0.655780:0.250644:0.661810:0.250644:0.661810:0.234175:0.655780:0.234175:0.000000 a b:@0.736848:0.250644:0.761989:0.250644:0.761989:0.234175:0.736848:0.234175:0.000000:0.000000:0.000000 :@0.766140:0.250016:0.780792:0.250016:0.780792:0.236642:0.766140:0.236642:0.000000 Z:@0.785117:0.249565:0.797967:0.249565:0.797967:0.236119:0.785117:0.236119:0.000000 +:@0.798063:0.241667:0.804364:0.241667:0.804364:0.232048:0.798063:0.232048:0.000000 , tal que:@0.804364:0.250534:0.860406:0.250534:0.860406:0.234037:0.804364:0.234037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404244:0.275013:0.408386:0.275013:0.408386:0.258516:0.404244:0.258516:0.000000 r:@0.427979:0.275129:0.434009:0.275129:0.434009:0.258660:0.427979:0.258660:0.000000 = 0,525252… . En primer lugar, al número = 0,525252… lo expre-:@0.434009:0.275013:0.891768:0.275013:0.891768:0.258516:0.434009:0.258516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 r:@0.726087:0.275129:0.732117:0.275129:0.732117:0.258660:0.726087:0.258660:0.000000 samos como::@0.427979:0.292364:0.521665:0.292364:0.521665:0.275866:0.427979:0.275866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404244:0.316843:0.408386:0.316843:0.408386:0.300345:0.404244:0.300345:0.000000 r:@0.427979:0.316959:0.434009:0.316959:0.434009:0.300490:0.427979:0.300490:0.000000 = 0,525252 … = + + + … = 1 + + + … .:@0.434009:0.316843:0.891965:0.316843:0.891965:0.300345:0.434009:0.300345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404244:0.334194:0.412528:0.334194:0.412528:0.317696:0.404244:0.317696:0.000000:0.000000 Ponemos = . Se define: S = = = .:@0.404244:0.358673:0.819890:0.358673:0.819890:0.342175:0.404244:0.342175:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.474870:0.358788:0.484040:0.358788:0.484040:0.342320:0.474870:0.342320:0.000000 Para :@0.404244:0.404059:0.471119:0.404066:0.471119:0.387568:0.404244:0.387562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.438729:0.404175:0.448091:0.404175:0.448091:0.387706:0.438729:0.387706:0.000000 :@0.452237:0.403547:0.466889:0.403547:0.466889:0.390174:0.452237:0.390174:0.000000 Z:@0.471216:0.403097:0.484066:0.403097:0.484066:0.389650:0.471216:0.389650:0.000000 +:@0.484167:0.395198:0.490468:0.395198:0.490468:0.385580:0.484167:0.385580:0.000000 , la suma de los + 1 primeros términos de la progresión :@0.490469:0.404066:0.895845:0.404066:0.895845:0.387568:0.490469:0.387568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.601512:0.404181:0.610875:0.404181:0.610875:0.387713:0.601512:0.387713:0.000000 geométrica de constante está dada como::@0.404238:0.421416:0.714902:0.421416:0.714902:0.404919:0.404238:0.404919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.585135:0.421532:0.594305:0.421532:0.594305:0.405063:0.585135:0.405063:0.000000 S:@0.404238:0.453139:0.412117:0.453139:0.412117:0.436671:0.404238:0.436671:0.000000 n:@0.412038:0.456368:0.417496:0.456368:0.417496:0.446767:0.412038:0.446767:0.000000 = 1 + + + … = = – .:@0.417497:0.453023:0.772369:0.453023:0.772369:0.436525:0.417497:0.436525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d d:@0.464177:0.453138:0.501609:0.453138:0.501609:0.436669:0.464177:0.436669:0.000000:0.000000:0.000000 2:@0.501608:0.446671:0.506561:0.446671:0.506561:0.437053:0.501608:0.437053:0.000000 d:@0.544842:0.453138:0.554012:0.453138:0.554012:0.436669:0.544842:0.436669:0.000000 n:@0.553934:0.446738:0.559393:0.446738:0.559393:0.437137:0.553934:0.437137:0.000000 Entonces, :@0.404229:0.505075:0.476376:0.505075:0.476376:0.488577:0.404229:0.488577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.476376:0.505190:0.485546:0.505190:0.485546:0.488722:0.476376:0.488722:0.000000 n:@0.485477:0.498791:0.490936:0.498791:0.490936:0.489189:0.485477:0.489189:0.000000 +1:@0.490936:0.498723:0.502190:0.498723:0.502190:0.489105:0.490936:0.489105:0.000000:0.000000 = = .:@0.502189:0.505075:0.650821:0.505075:0.650821:0.488577:0.502189:0.488577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404245:0.522426:0.408387:0.522426:0.408387:0.505928:0.404245:0.505928:0.000000 La sucesión es positiva, estrictamente decreciente.:@0.404245:0.546905:0.812468:0.546905:0.812468:0.530407:0.404245:0.530407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para suficientemente grande, es positivo y tiende o se:@0.404245:0.581606:0.858149:0.581606:0.858149:0.565108:0.404245:0.565108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.438729:0.581722:0.448092:0.581722:0.448092:0.565253:0.438729:0.565253:0.000000 aproxima cada vez a 0, lo que se escribe 0.:@0.404245:0.616308:0.789247:0.616308:0.789247:0.599811:0.404245:0.599810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 → :@0.755242:0.623382:0.773853:0.623382:0.773853:0.605247:0.755242:0.605247:0.000000:0.000000 Luego, para suficientemente grande:@0.404231:0.633659:0.670801:0.633659:0.670801:0.617161:0.404231:0.617161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.489711:0.633775:0.499074:0.633775:0.499074:0.617306:0.489711:0.617306:0.000000 = = 0,:@0.533212:0.686174:0.762795:0.686180:0.762795:0.669683:0.533212:0.669676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 → :@0.728789:0.693254:0.747399:0.693254:0.747399:0.675119:0.728789:0.675119:0.000000:0.000000 y en consecuencia, = – ,:@0.404230:0.738232:0.716741:0.738232:0.716741:0.721735:0.404230:0.721735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.541089:0.738348:0.548968:0.738348:0.548968:0.721879:0.541089:0.721879:0.000000 n:@0.548896:0.741577:0.554355:0.741577:0.554355:0.731975:0.548896:0.731975:0.000000 → :@0.683353:0.745307:0.701963:0.745307:0.701963:0.727171:0.683353:0.727171:0.000000:0.000000 S:@0.706107:0.738348:0.713986:0.738348:0.713986:0.721879:0.706107:0.721879:0.000000 siendo = 1 + + + … + + … = . :@0.404240:0.772934:0.783786:0.772934:0.783786:0.756436:0.404240:0.756436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.459531:0.773050:0.467410:0.773050:0.467410:0.756581:0.459531:0.756581:0.000000 d d:@0.514090:0.773050:0.551522:0.773050:0.551522:0.756581:0.514090:0.756581:0.000000:0.000000:0.000000 2:@0.551517:0.766581:0.556470:0.766581:0.556470:0.756963:0.551517:0.756963:0.000000 d:@0.609700:0.773050:0.618870:0.773050:0.618870:0.756581:0.609700:0.756581:0.000000 n:@0.618793:0.766648:0.624251:0.766648:0.624251:0.757047:0.618793:0.757047:0.000000 Así, = 1 + + + … = × = :@0.404241:0.807635:0.770532:0.807635:0.770532:0.791138:0.404241:0.791138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 r:@0.433351:0.807751:0.439381:0.807751:0.439381:0.791282:0.433351:0.791282:0.000000 es el número racional buscado. Por lo tanto,:@0.404241:0.842337:0.714947:0.842337:0.714947:0.825839:0.404241:0.825839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.404241:0.877154:0.413450:0.877154:0.413450:0.860685:0.404241:0.860685:0.000000 = 3,525252… = 3 + 0,525252… = 3 + = .:@0.413450:0.877038:0.761438:0.877038:0.761438:0.860541:0.413450:0.860541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para verificar este resultado, basta dividir 349 para 99.:@0.404241:0.911740:0.780158:0.911740:0.780158:0.895242:0.404241:0.895242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 3:@0.448489:0.173177:0.480650:0.173177:0.480650:0.156680:0.448489:0.156680:0.000000:0.000000:0.000000 2 2:@0.448489:0.189516:0.480650:0.189516:0.480650:0.173018:0.448489:0.173018:0.000000:0.000000:0.000000 1 3:@0.614338:0.173177:0.646498:0.173177:0.646498:0.156680:0.614338:0.156680:0.000000:0.000000:0.000000 2 2:@0.614338:0.189516:0.646498:0.189516:0.646498:0.173018:0.614338:0.173018:0.000000:0.000000:0.000000 1:@0.689069:0.173177:0.697565:0.173177:0.697565:0.156680:0.689069:0.156680:0.000000 2:@0.689069:0.189516:0.697565:0.189516:0.697565:0.173018:0.689069:0.173018:0.000000 1 3:@0.513824:0.173177:0.545984:0.173177:0.545984:0.156680:0.513824:0.156680:0.000000:0.000000:0.000000 2 2:@0.513824:0.189516:0.545984:0.189516:0.545984:0.173018:0.513824:0.173018:0.000000:0.000000:0.000000 a:@0.685236:0.243137:0.694213:0.243137:0.694213:0.226669:0.685236:0.226669:0.000000 b:@0.685082:0.259476:0.694348:0.259476:0.694348:0.243007:0.685082:0.243007:0.000000 3:@0.790449:0.173177:0.798945:0.173177:0.798945:0.156680:0.790449:0.156680:0.000000 2:@0.790449:0.189516:0.798945:0.189516:0.798945:0.173018:0.790449:0.173018:0.000000 52:@0.558918:0.309500:0.576102:0.309500:0.576102:0.293003:0.558918:0.293003:0.000000:0.000000 10:@0.556394:0.325839:0.573579:0.325839:0.573579:0.309341:0.556394:0.309341:0.000000:0.000000 2:@0.573722:0.319492:0.578675:0.319492:0.578675:0.309874:0.573722:0.309874:0.000000 1:@0.791676:0.309500:0.800172:0.309500:0.800172:0.293003:0.791676:0.293003:0.000000 10:@0.784798:0.325839:0.801982:0.325839:0.801982:0.309341:0.784798:0.309341:0.000000:0.000000 2:@0.802136:0.319492:0.807089:0.319492:0.807089:0.309874:0.802136:0.309874:0.000000 1:@0.512279:0.351021:0.520775:0.351021:0.520775:0.334524:0.512279:0.334524:0.000000 10:@0.505401:0.367360:0.522586:0.367360:0.522586:0.350862:0.505401:0.350862:0.000000:0.000000 2:@0.522739:0.361013:0.527692:0.361013:0.527692:0.351395:0.522739:0.351395:0.000000 1:@0.613202:0.497658:0.621698:0.497658:0.621698:0.481160:0.613202:0.481160:0.000000 10:@0.594380:0.513997:0.611565:0.513997:0.611565:0.497499:0.594380:0.497499:0.000000:0.000000 2( +1):@0.611725:0.507651:0.640556:0.507651:0.640556:0.498033:0.611725:0.498033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.620317:0.507719:0.625775:0.507719:0.625775:0.498117:0.620317:0.498117:0.000000 1:@0.653251:0.574295:0.661746:0.574295:0.661746:0.557798:0.653251:0.557798:0.000000 10:@0.634428:0.590634:0.651613:0.590634:0.651613:0.574136:0.634428:0.574136:0.000000:0.000000 2( +1):@0.651771:0.584289:0.680603:0.584289:0.680603:0.574671:0.651771:0.574671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.660363:0.584356:0.665822:0.584356:0.665822:0.574755:0.660363:0.574755:0.000000 1:@0.713665:0.608699:0.722161:0.608699:0.722161:0.592201:0.713665:0.592201:0.000000 10:@0.694843:0.625038:0.712027:0.625038:0.712027:0.608540:0.694843:0.608540:0.000000:0.000000 2( +1):@0.712185:0.618691:0.741017:0.618691:0.741017:0.609073:0.712185:0.609073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.720778:0.618758:0.726236:0.618758:0.726236:0.609157:0.720778:0.609157:0.000000 1:@0.684882:0.678553:0.693378:0.678553:0.693378:0.662056:0.684882:0.662056:0.000000 99×10:@0.661186:0.694892:0.706556:0.694892:0.706556:0.678394:0.661186:0.678394:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.706706:0.688545:0.711659:0.688545:0.711659:0.678927:0.706706:0.678927:0.000000 n:@0.711715:0.688613:0.717174:0.688613:0.717174:0.679012:0.711715:0.679012:0.000000 1:@0.654820:0.351021:0.663316:0.351021:0.663316:0.334524:0.654820:0.334524:0.000000 1 – :@0.640757:0.367360:0.668325:0.367360:0.668325:0.350862:0.640757:0.350862:0.000000:0.000000:0.000000:0.000000 d:@0.668325:0.367476:0.677495:0.367476:0.677495:0.351007:0.668325:0.351007:0.000000 d:@0.583904:0.445583:0.593074:0.445583:0.593074:0.429114:0.583904:0.429114:0.000000 n:@0.592997:0.439182:0.598456:0.439182:0.598456:0.429581:0.592997:0.429581:0.000000 +1:@0.598456:0.439114:0.609710:0.439114:0.609710:0.429496:0.598456:0.429496:0.000000:0.000000 – 1:@0.609709:0.445467:0.636989:0.445467:0.636989:0.428970:0.609709:0.428970:0.000000:0.000000:0.000000:0.000000 d:@0.592217:0.461922:0.601387:0.461922:0.601387:0.445453:0.592217:0.445453:0.000000 – 1:@0.601387:0.461806:0.628666:0.461806:0.628666:0.445308:0.601387:0.445308:0.000000:0.000000:0.000000:0.000000 d:@0.494166:0.678669:0.503337:0.678669:0.503337:0.662200:0.494166:0.662200:0.000000 n:@0.503260:0.672268:0.508718:0.672268:0.508718:0.662667:0.503260:0.662667:0.000000 +1:@0.508718:0.672200:0.519972:0.672200:0.519972:0.662582:0.508718:0.662582:0.000000:0.000000 1 – :@0.488846:0.694898:0.516125:0.694898:0.516125:0.678401:0.488846:0.678401:0.000000:0.000000:0.000000:0.000000 d:@0.516125:0.695014:0.525296:0.695014:0.525296:0.678545:0.516125:0.678545:0.000000 d:@0.731890:0.445583:0.741060:0.445583:0.741060:0.429114:0.731890:0.429114:0.000000 n:@0.740983:0.439182:0.746441:0.439182:0.746441:0.429581:0.740983:0.429581:0.000000 +1:@0.746441:0.439114:0.757696:0.439114:0.757696:0.429496:0.746441:0.429496:0.000000:0.000000 1 – :@0.726472:0.461812:0.754040:0.461812:0.754040:0.445315:0.726472:0.445315:0.000000:0.000000:0.000000:0.000000 d:@0.754040:0.461928:0.763211:0.461928:0.763211:0.445459:0.754040:0.445459:0.000000 1:@0.680530:0.445467:0.689026:0.445467:0.689026:0.428970:0.680530:0.428970:0.000000 1 – :@0.666466:0.461806:0.694035:0.461806:0.694035:0.445308:0.666466:0.445308:0.000000:0.000000:0.000000:0.000000 d:@0.694035:0.461922:0.703205:0.461922:0.703205:0.445453:0.694035:0.445453:0.000000 1:@0.727998:0.351021:0.736494:0.351021:0.736494:0.334524:0.727998:0.334524:0.000000 1:@0.836907:0.309500:0.845403:0.309500:0.845403:0.293003:0.836907:0.293003:0.000000 10:@0.830029:0.325839:0.847214:0.325839:0.847214:0.309341:0.830029:0.309341:0.000000:0.000000 4:@0.847367:0.319492:0.852320:0.319492:0.852320:0.309874:0.847367:0.309874:0.000000 52:@0.602000:0.309500:0.619185:0.309500:0.619185:0.293003:0.602000:0.293003:0.000000:0.000000 10:@0.599476:0.325839:0.616661:0.325839:0.616661:0.309341:0.599476:0.309341:0.000000:0.000000 4:@0.616804:0.319492:0.621757:0.319492:0.621757:0.309874:0.616804:0.309874:0.000000 52:@0.645895:0.309500:0.663079:0.309500:0.663079:0.293003:0.645895:0.293003:0.000000:0.000000 10:@0.643371:0.325839:0.660555:0.325839:0.660555:0.309341:0.643371:0.309341:0.000000:0.000000 6:@0.660699:0.319492:0.665652:0.319492:0.665652:0.309874:0.660699:0.309874:0.000000 100:@0.787630:0.351021:0.813503:0.351021:0.813503:0.334524:0.787630:0.334524:0.000000:0.000000:0.000000 99:@0.791984:0.367360:0.809168:0.367360:0.809168:0.350862:0.791984:0.350862:0.000000:0.000000 52:@0.724076:0.309500:0.741261:0.309500:0.741261:0.293003:0.724076:0.293003:0.000000:0.000000 10:@0.721553:0.325839:0.738737:0.325839:0.738737:0.309341:0.721553:0.309341:0.000000:0.000000 2:@0.738880:0.319492:0.743834:0.319492:0.743834:0.309874:0.738880:0.309874:0.000000 3:@0.717699:0.157760:0.726195:0.157760:0.726195:0.141263:0.717699:0.141263:0.000000 2:@0.717699:0.174099:0.726195:0.174099:0.726195:0.157601:0.717699:0.157601:0.000000 3:@0.717704:0.190096:0.726200:0.190096:0.726200:0.173598:0.717704:0.173598:0.000000 2:@0.717704:0.206434:0.726200:0.206434:0.726200:0.189937:0.717704:0.189937:0.000000 0:@0.487430:0.162781:0.492168:0.162781:0.492168:0.153581:0.487430:0.153581:0.000000 n:@0.653275:0.162845:0.658496:0.162845:0.658496:0.153661:0.653275:0.153661:0.000000 –1:@0.658496:0.162781:0.669089:0.162781:0.669089:0.153581:0.658496:0.153581:0.000000:0.000000 1:@0.552760:0.162781:0.557498:0.162781:0.557498:0.153581:0.552760:0.153581:0.000000 n:@0.805722:0.162845:0.810944:0.162845:0.810944:0.153661:0.805722:0.153661:0.000000 n:@0.732969:0.147429:0.738190:0.147429:0.738190:0.138245:0.732969:0.138245:0.000000 – 1:@0.736749:0.197591:0.759887:0.197591:0.759887:0.181093:0.736749:0.181093:0.000000:0.000000:0.000000 – 1:@0.738156:0.165231:0.761293:0.165231:0.761293:0.148734:0.738156:0.148734:0.000000:0.000000:0.000000 1:@0.742929:0.368841:0.751425:0.368841:0.751425:0.352344:0.742929:0.352344:0.000000 10:@0.736052:0.385180:0.753236:0.385180:0.753236:0.368682:0.736052:0.368682:0.000000:0.000000 2:@0.753388:0.378833:0.758341:0.378833:0.758341:0.369215:0.753388:0.369215:0.000000 1 –:@0.707528:0.376335:0.730666:0.376335:0.730666:0.359837:0.707528:0.359837:0.000000:0.000000:0.000000 1:@0.534146:0.497658:0.542642:0.497658:0.542642:0.481160:0.534146:0.481160:0.000000 10:@0.527268:0.513997:0.544453:0.513997:0.544453:0.497499:0.527268:0.497499:0.000000:0.000000 2:@0.544606:0.507651:0.549559:0.507651:0.549559:0.498033:0.544606:0.498033:0.000000 1:@0.509823:0.539149:0.518319:0.539149:0.518319:0.522651:0.509823:0.522651:0.000000 10:@0.500210:0.555488:0.517394:0.555488:0.517394:0.538990:0.500210:0.538990:0.000000:0.000000 2:@0.517553:0.549142:0.522506:0.549142:0.522506:0.539524:0.517553:0.539524:0.000000 n:@0.522562:0.549210:0.528021:0.549210:0.528021:0.539608:0.522562:0.539608:0.000000 n:@0.556172:0.488167:0.561393:0.488167:0.561393:0.478983:0.556172:0.478983:0.000000 +1:@0.561393:0.488102:0.572158:0.488102:0.572158:0.478902:0.561393:0.478902:0.000000:0.000000 n:@0.747645:0.622279:0.753751:0.622279:0.753751:0.611539:0.747645:0.611539:0.000000 →:@0.753751:0.621597:0.764499:0.621597:0.764499:0.611586:0.753751:0.611586:0.000000 ∞:@0.764496:0.622204:0.773178:0.622204:0.773178:0.611444:0.764496:0.611444:0.000000 n:@0.728651:0.690890:0.734757:0.690890:0.734757:0.680150:0.728651:0.680150:0.000000 →:@0.734761:0.690204:0.745508:0.690204:0.745508:0.680193:0.734761:0.680193:0.000000 ∞:@0.745506:0.690811:0.754188:0.690811:0.754188:0.680051:0.745506:0.680051:0.000000 n:@0.678777:0.743806:0.684883:0.743806:0.684883:0.733066:0.678777:0.733066:0.000000 →:@0.684882:0.743120:0.695630:0.743120:0.695630:0.733109:0.684882:0.733109:0.000000 ∞:@0.695627:0.743727:0.704309:0.743727:0.704309:0.732968:0.695627:0.732968:0.000000 1:@0.601211:0.696016:0.609707:0.696016:0.609707:0.679518:0.601211:0.679518:0.000000 10:@0.594333:0.712355:0.611518:0.712355:0.611518:0.695857:0.594333:0.695857:0.000000:0.000000 2:@0.611671:0.706009:0.616624:0.706009:0.616624:0.696391:0.611671:0.696391:0.000000 1 –:@0.565810:0.703511:0.588947:0.703511:0.588947:0.687013:0.565810:0.687013:0.000000:0.000000:0.000000 1:@0.581312:0.661727:0.589808:0.661727:0.589808:0.645229:0.581312:0.645229:0.000000 10:@0.574435:0.678066:0.591619:0.678066:0.591619:0.661568:0.574435:0.661568:0.000000:0.000000 2:@0.591773:0.671719:0.596726:0.671719:0.596726:0.662101:0.591773:0.662101:0.000000 n:@0.603338:0.652234:0.608560:0.652234:0.608560:0.643051:0.603338:0.643051:0.000000 +1:@0.608560:0.652170:0.619324:0.652170:0.619324:0.642970:0.608560:0.642970:0.000000:0.000000 1:@0.589340:0.730765:0.597836:0.730765:0.597836:0.714268:0.589340:0.714268:0.000000 1 – :@0.575276:0.747104:0.602845:0.747104:0.602845:0.730606:0.575276:0.730606:0.000000:0.000000:0.000000:0.000000 d:@0.602845:0.747220:0.612015:0.747220:0.612015:0.730751:0.602845:0.730751:0.000000 1:@0.695857:0.765515:0.704353:0.765515:0.704353:0.749017:0.695857:0.749017:0.000000 1 – :@0.681793:0.781853:0.709362:0.781853:0.709362:0.765356:0.681793:0.765356:0.000000:0.000000:0.000000:0.000000 d:@0.709362:0.781969:0.718532:0.781969:0.718532:0.765500:0.709362:0.765500:0.000000 d:@0.640334:0.730881:0.649505:0.730881:0.649505:0.714412:0.640334:0.714412:0.000000 n:@0.649428:0.724481:0.654886:0.724481:0.654886:0.714880:0.649428:0.714880:0.000000 +1:@0.654886:0.724414:0.666140:0.724414:0.666140:0.714795:0.654886:0.714795:0.000000:0.000000 1 – :@0.634917:0.747110:0.662485:0.747110:0.662485:0.730613:0.634917:0.730613:0.000000:0.000000:0.000000:0.000000 d:@0.662485:0.747226:0.671656:0.747226:0.671656:0.730757:0.662485:0.730757:0.000000 52:@0.770645:0.800085:0.787829:0.800085:0.787829:0.783588:0.770645:0.783588:0.000000:0.000000 99:@0.770645:0.816424:0.787829:0.816424:0.787829:0.799926:0.770645:0.799926:0.000000:0.000000 52:@0.684455:0.869584:0.701640:0.869584:0.701640:0.853086:0.684455:0.853086:0.000000:0.000000 99:@0.684455:0.885923:0.701640:0.885923:0.701640:0.869425:0.684455:0.869425:0.000000:0.000000 52:@0.463510:0.800085:0.480694:0.800085:0.480694:0.783588:0.463510:0.783588:0.000000:0.000000 10:@0.460986:0.816424:0.478170:0.816424:0.478170:0.799926:0.460986:0.799926:0.000000:0.000000 2:@0.478312:0.810077:0.483265:0.810077:0.483265:0.800459:0.478312:0.800459:0.000000 52:@0.672162:0.800085:0.689347:0.800085:0.689347:0.783588:0.672162:0.783588:0.000000:0.000000 10:@0.669639:0.816424:0.686823:0.816424:0.686823:0.799926:0.669639:0.799926:0.000000:0.000000 2:@0.686966:0.810077:0.691920:0.810077:0.691920:0.800459:0.686966:0.800459:0.000000 100:@0.717514:0.800085:0.743388:0.800085:0.743388:0.783588:0.717514:0.783588:0.000000:0.000000:0.000000 99:@0.721868:0.816424:0.739053:0.816424:0.739053:0.799926:0.721868:0.799926:0.000000:0.000000 349:@0.728785:0.869584:0.754659:0.869584:0.754659:0.853086:0.728785:0.853086:0.000000:0.000000:0.000000 99:@0.733139:0.885923:0.750324:0.885923:0.750324:0.869425:0.733139:0.869425:0.000000:0.000000 1:@0.533689:0.800085:0.542185:0.800085:0.542185:0.783588:0.533689:0.783588:0.000000 10:@0.526811:0.816424:0.543996:0.816424:0.543996:0.799926:0.526811:0.799926:0.000000:0.000000 2:@0.544149:0.810077:0.549102:0.810077:0.549102:0.800459:0.544149:0.800459:0.000000 1:@0.582217:0.800085:0.590713:0.800085:0.590713:0.783588:0.582217:0.783588:0.000000 10:@0.575339:0.816424:0.592524:0.816424:0.592524:0.799926:0.575339:0.799926:0.000000:0.000000 4:@0.592676:0.810077:0.597629:0.810077:0.597629:0.800459:0.592676:0.800459:0.000000 Competencia :@0.199644:0.247601:0.297267:0.247601:0.297267:0.232129:0.199644:0.232129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 socioemocional:@0.199644:0.260169:0.310020:0.260169:0.310020:0.244697:0.199644:0.244697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muchas veces nos :@0.199880:0.284644:0.321777:0.284644:0.321777:0.269580:0.199880:0.269580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 hemos preguntado “¿para :@0.153337:0.300486:0.324555:0.300486:0.324555:0.285422:0.153337:0.285422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 qué me va a servir tal o cual :@0.153337:0.316327:0.337380:0.316327:0.337380:0.301264:0.153337:0.301264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tema que aprendo en el aula?”. :@0.153337:0.332169:0.353281:0.332169:0.353281:0.317106:0.153337:0.317106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Analizando las cosas de forma :@0.153337:0.348011:0.352314:0.348011:0.352314:0.332948:0.153337:0.332948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diferente, podremos entender :@0.153337:0.363853:0.350657:0.363853:0.350657:0.348790:0.153337:0.348790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que, por ejemplo, la matemáti-:@0.153337:0.379695:0.352349:0.379695:0.352349:0.364632:0.153337:0.364632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ca nos sirve para lo más simple :@0.153337:0.395537:0.357186:0.395537:0.357186:0.380474:0.153337:0.380474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (saber cuánto dinero tenemos :@0.153337:0.411379:0.352894:0.411379:0.352894:0.396316:0.153337:0.396316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en el bolsillo) y también para :@0.153337:0.427221:0.344590:0.427221:0.344590:0.412158:0.153337:0.412158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lo más complejo (determinar :@0.153337:0.443063:0.346175:0.443063:0.346175:0.428000:0.153337:0.428000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el número de bacterias que se :@0.153337:0.458905:0.350590:0.458905:0.350590:0.443842:0.153337:0.443842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 reproducen en un laboratorio). :@0.153337:0.474747:0.357732:0.474747:0.357732:0.459684:0.153337:0.459684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De forma particular, las progre-:@0.153337:0.490589:0.353703:0.490589:0.353703:0.475526:0.153337:0.475526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 siones geométricas nos permi-:@0.153337:0.506431:0.350556:0.506431:0.350556:0.491368:0.153337:0.491368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ten determinar los intereses de :@0.153337:0.522273:0.356322:0.522273:0.356322:0.507210:0.153337:0.507210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 nuestros ahorros, o el beneficio :@0.153337:0.538115:0.359049:0.538115:0.359049:0.523052:0.153337:0.523052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 o utilidad de un capital inicial :@0.153337:0.553957:0.348233:0.553957:0.348233:0.538894:0.153337:0.538894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 puesto a una tasa de interés :@0.153337:0.569799:0.338015:0.569799:0.338015:0.554736:0.153337:0.554736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 durante un tiempo. :@0.153337:0.585641:0.283662:0.585641:0.283662:0.570578:0.153337:0.570578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Confecciona:@0.153344:0.723398:0.240608:0.723398:0.240608:0.707925:0.153344:0.707925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un resumen en :@0.240608:0.722975:0.349453:0.722975:0.349453:0.707912:0.240608:0.707912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el cuaderno acerca de la impor-:@0.153344:0.738817:0.357265:0.738817:0.357265:0.723754:0.153344:0.723754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tancia de la matemática en tu :@0.153344:0.754659:0.349699:0.754659:0.349699:0.739596:0.153344:0.739596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vida personal.:@0.153344:0.770501:0.241980:0.770501:0.241980:0.755438:0.153344:0.755438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Shutterstock, 142344334:@0.139924:0.693209:0.139924:0.625036:0.128455:0.625036:0.128455:0.693209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000