123:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000
Suma de los primeros términos de una progresión geométrica:@0.108233:0.100892:0.595778:0.100892:0.595778:0.083209:0.108233:0.083209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.108233:0.117600:0.146031:0.117600:0.146031:0.101102:0.108233:0.101102:0.000000:0.000000:0.000000:0.000000:0.000000
a, d:@0.146475:0.117715:0.172030:0.117715:0.172030:0.101247:0.146475:0.101247:0.000000:0.000000:0.000000:0.000000
     no nulos y      , la progresión geométrica ( ) defi-:@0.172136:0.117600:0.595758:0.117600:0.595758:0.101102:0.172136:0.101102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.176791:0.117081:0.191443:0.117081:0.191443:0.103708:0.176791:0.103708:0.000000
R:@0.196212:0.116631:0.210122:0.116631:0.210122:0.103184:0.196212:0.103184:0.000000
n:@0.294485:0.117715:0.303847:0.117715:0.303847:0.101247:0.294485:0.101247:0.000000
:@0.308590:0.117081:0.323243:0.117081:0.323243:0.103708:0.308590:0.103708:0.000000
N:@0.328012:0.116631:0.343000:0.116631:0.343000:0.103184:0.328012:0.103184:0.000000
u:@0.537984:0.117715:0.547193:0.117715:0.547193:0.101247:0.537984:0.101247:0.000000
n:@0.547127:0.120945:0.552586:0.120945:0.552586:0.111344:0.547127:0.111344:0.000000
nida como   = :@0.108231:0.134951:0.221932:0.134951:0.221932:0.118453:0.108231:0.118453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.188566:0.135066:0.197774:0.135066:0.197774:0.118597:0.188566:0.118597:0.000000
n:@0.197729:0.138296:0.203188:0.138296:0.203188:0.128695:0.197729:0.128695:0.000000
ad:@0.221527:0.135066:0.239636:0.135066:0.239636:0.118597:0.221527:0.118597:0.000000:0.000000
n:@0.239570:0.128666:0.245029:0.128666:0.245029:0.119065:0.239570:0.119065:0.000000
,   :@0.245028:0.134951:0.259400:0.134951:0.259400:0.118453:0.245028:0.118453:0.000000:0.000000:0.000000:0.000000
∀:@0.259011:0.142537:0.270584:0.142537:0.270584:0.123538:0.259011:0.123538:0.000000
n:@0.270683:0.135066:0.280046:0.135066:0.280046:0.118597:0.270683:0.118597:0.000000
    . Consideramos la suma de los primeros :@0.280142:0.134951:0.599872:0.134951:0.599872:0.118453:0.280142:0.118453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.283982:0.134432:0.298635:0.134432:0.298635:0.121059:0.283982:0.121059:0.000000
N:@0.302555:0.133982:0.317543:0.133982:0.317543:0.120535:0.302555:0.120535:0.000000
n:@0.108226:0.152417:0.117589:0.152417:0.117589:0.135948:0.108226:0.135948:0.000000
 + 1 términos de esta progresión::@0.117589:0.152301:0.350522:0.152301:0.350522:0.135804:0.117589:0.135804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.277606:0.176896:0.285486:0.176896:0.285486:0.160427:0.277606:0.160427:0.000000
n:@0.285413:0.180125:0.290872:0.180125:0.290872:0.170524:0.285413:0.170524:0.000000
 =   +   + … + :@0.290873:0.176780:0.411781:0.176780:0.411781:0.160282:0.290873:0.160282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.309965:0.176895:0.319173:0.176895:0.319173:0.160427:0.309965:0.160427:0.000000
0:@0.319270:0.180058:0.324223:0.180058:0.324223:0.170439:0.319270:0.170439:0.000000
u:@0.343660:0.176895:0.352868:0.176895:0.352868:0.160427:0.343660:0.160427:0.000000
1:@0.352964:0.180058:0.357917:0.180058:0.357917:0.170439:0.352964:0.170439:0.000000
u:@0.411877:0.176895:0.421086:0.176895:0.421086:0.160427:0.411877:0.160427:0.000000
n:@0.420932:0.180125:0.426390:0.180125:0.426390:0.170524:0.420932:0.170524:0.000000
=   +   + :@0.202474:0.201259:0.282694:0.201259:0.282694:0.184762:0.202474:0.184762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a ad ad:@0.217423:0.201375:0.300804:0.201375:0.300804:0.184906:0.217423:0.184906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.300802:0.194906:0.305755:0.194906:0.305755:0.185288:0.300802:0.185288:0.000000
 + … + :@0.305756:0.201259:0.358985:0.201259:0.358985:0.184762:0.305756:0.184762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad:@0.358985:0.201375:0.377095:0.201375:0.377095:0.184906:0.358985:0.184906:0.000000:0.000000
n:@0.377017:0.194974:0.382475:0.194974:0.382475:0.185373:0.377017:0.185373:0.000000
–1:@0.382475:0.194906:0.393550:0.194906:0.393550:0.185288:0.382475:0.185288:0.000000:0.000000
 + :@0.393550:0.201259:0.412642:0.201259:0.412642:0.184762:0.393550:0.184762:0.000000:0.000000:0.000000
ad:@0.412642:0.201375:0.430751:0.201375:0.430751:0.184906:0.412642:0.184906:0.000000:0.000000
n:@0.430673:0.194974:0.436132:0.194974:0.436132:0.185373:0.430673:0.185373:0.000000
 = :@0.436131:0.201259:0.455223:0.201259:0.455223:0.184762:0.436131:0.184762:0.000000:0.000000:0.000000
a     d:@0.455223:0.201375:0.494081:0.201375:0.494081:0.184906:0.455223:0.184906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.493965:0.194974:0.498772:0.194974:0.498772:0.185373:0.493965:0.185373:0.000000
.:@0.498772:0.201259:0.501527:0.201259:0.501527:0.184762:0.498772:0.184762:0.000000
Si multiplicamos a   por  , tenemos: :@0.108226:0.235961:0.374693:0.235961:0.374693:0.219463:0.108226:0.219463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.242368:0.236076:0.250248:0.236076:0.250248:0.219608:0.242368:0.219608:0.000000
n:@0.250178:0.239305:0.255636:0.239305:0.255636:0.229704:0.250178:0.229704:0.000000
d:@0.289215:0.236076:0.298385:0.236076:0.298385:0.219608:0.289215:0.219608:0.000000
dS:@0.213368:0.260556:0.230417:0.260556:0.230417:0.244087:0.213368:0.244087:0.000000:0.000000
n:@0.230348:0.263785:0.235807:0.263785:0.235807:0.254183:0.230348:0.254183:0.000000
 =   + :@0.235808:0.260439:0.292101:0.260439:0.292101:0.243942:0.235808:0.243942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad ad:@0.254899:0.260555:0.310210:0.260555:0.310210:0.244086:0.254899:0.244086:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.310208:0.254086:0.315162:0.254086:0.315162:0.244468:0.310208:0.244468:0.000000
 + :@0.315160:0.260439:0.334252:0.260439:0.334252:0.243942:0.315160:0.243942:0.000000:0.000000:0.000000
ad:@0.334252:0.260555:0.352362:0.260555:0.352362:0.244086:0.334252:0.244086:0.000000:0.000000
3:@0.352362:0.254086:0.357316:0.254086:0.357316:0.244468:0.352362:0.244468:0.000000
 + … + :@0.357314:0.260439:0.410544:0.260439:0.410544:0.243942:0.357314:0.243942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad:@0.410544:0.260555:0.428654:0.260555:0.428654:0.244086:0.410544:0.244086:0.000000:0.000000
n:@0.428576:0.254154:0.434034:0.254154:0.434034:0.244552:0.428576:0.244552:0.000000
 + :@0.434034:0.260439:0.453126:0.260439:0.453126:0.243942:0.434034:0.243942:0.000000:0.000000:0.000000
ad:@0.453126:0.260555:0.471235:0.260555:0.471235:0.244086:0.453126:0.244086:0.000000:0.000000
n:@0.471159:0.254154:0.476617:0.254154:0.476617:0.244552:0.471159:0.244552:0.000000
+1:@0.476617:0.254086:0.487871:0.254086:0.487871:0.244468:0.476617:0.244468:0.000000:0.000000
.:@0.487871:0.260439:0.490626:0.260439:0.490626:0.243942:0.487871:0.243942:0.000000
Luego, :@0.108230:0.295141:0.158339:0.295141:0.158339:0.278643:0.108230:0.278643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dS:@0.158339:0.295256:0.175388:0.295256:0.175388:0.278788:0.158339:0.278788:0.000000:0.000000
n:@0.175313:0.298486:0.180772:0.298486:0.180772:0.288885:0.175313:0.288885:0.000000
 –   = :@0.180773:0.295141:0.231908:0.295141:0.231908:0.278643:0.180773:0.278643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.199556:0.295256:0.207436:0.295256:0.207436:0.278788:0.199556:0.278788:0.000000
n:@0.207359:0.298486:0.212817:0.298486:0.212817:0.288885:0.207359:0.288885:0.000000
ad:@0.231908:0.295256:0.250018:0.295256:0.250018:0.278788:0.231908:0.278788:0.000000:0.000000
n:@0.249940:0.288856:0.255399:0.288856:0.255399:0.279255:0.249940:0.279255:0.000000
+1:@0.255399:0.288789:0.266653:0.288789:0.266653:0.279171:0.255399:0.279171:0.000000:0.000000
 –   =  (:@0.266652:0.295141:0.328436:0.295141:0.328436:0.278643:0.266652:0.278643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a a d:@0.285436:0.295256:0.337606:0.295256:0.337606:0.278788:0.285436:0.278788:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.337528:0.288856:0.342987:0.288856:0.342987:0.279255:0.337528:0.279255:0.000000
+1:@0.342987:0.288789:0.354241:0.288789:0.354241:0.279171:0.342987:0.279171:0.000000:0.000000
 – 1), o lo que es lo mismo, :@0.354240:0.295141:0.548721:0.295141:0.548721:0.278643:0.354240:0.278643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  – 1)  =  (:@0.273288:0.319620:0.368924:0.319619:0.368924:0.303121:0.273288:0.303122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.279241:0.319735:0.288411:0.319735:0.288411:0.303267:0.279241:0.303267:0.000000
S:@0.321644:0.319735:0.329523:0.319735:0.329523:0.303267:0.321644:0.303267:0.000000
n:@0.329443:0.322965:0.334902:0.322965:0.334902:0.313363:0.329443:0.313363:0.000000
a d:@0.353993:0.319735:0.378094:0.319735:0.378094:0.303266:0.353993:0.303266:0.000000:0.000000:0.000000
n:@0.378017:0.313335:0.383476:0.313335:0.383476:0.303734:0.378017:0.303734:0.000000
+1:@0.383476:0.313267:0.394730:0.313267:0.394730:0.303649:0.383476:0.303649:0.000000:0.000000
 – 1).:@0.394729:0.319619:0.430717:0.319619:0.430717:0.303121:0.394729:0.303121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108236:0.336970:0.112378:0.336970:0.112378:0.320472:0.108236:0.320472:0.000000
Si   = 1, entonces ( ) es la sucesión constante  , en cuyo caso:@0.108236:0.354321:0.549892:0.354321:0.549892:0.337823:0.108236:0.337823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.124187:0.354436:0.133357:0.354436:0.133357:0.337968:0.124187:0.337968:0.000000
u:@0.242746:0.354436:0.251954:0.354436:0.251954:0.337968:0.242746:0.337968:0.000000
n:@0.251892:0.357666:0.257350:0.357666:0.257350:0.348065:0.251892:0.348065:0.000000
a:@0.441582:0.354436:0.450560:0.354436:0.450560:0.337968:0.441582:0.337968:0.000000
S:@0.108236:0.371787:0.116115:0.371787:0.116115:0.355318:0.108236:0.355318:0.000000
n:@0.116035:0.375017:0.121494:0.375017:0.121494:0.365416:0.116035:0.365416:0.000000
 = (  + 1) . Si   ≠ 1, entonces :@0.121494:0.371671:0.333778:0.371671:0.333778:0.355174:0.121494:0.355174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.146539:0.371787:0.155902:0.371787:0.155902:0.355318:0.146539:0.355318:0.000000
a:@0.189443:0.371787:0.198420:0.371787:0.198420:0.355318:0.189443:0.355318:0.000000
d:@0.221269:0.371787:0.230439:0.371787:0.230439:0.355318:0.221269:0.355318:0.000000
S:@0.218283:0.399823:0.226162:0.399823:0.226162:0.383354:0.218283:0.383354:0.000000
n:@0.226086:0.403060:0.231545:0.403060:0.231545:0.393458:0.226086:0.393458:0.000000
 = :@0.231544:0.399714:0.250636:0.399714:0.250636:0.383217:0.231544:0.383217:0.000000:0.000000:0.000000
a     d:@0.250636:0.399830:0.289494:0.399830:0.289494:0.383361:0.250636:0.383361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.289378:0.393430:0.294185:0.393430:0.294185:0.383829:0.289378:0.383829:0.000000
 =                   = :@0.294185:0.399714:0.407618:0.399714:0.407618:0.383217:0.294185:0.383217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.313277:0.399830:0.322254:0.399830:0.322254:0.383361:0.313277:0.383361:0.000000
a                .:@0.407618:0.399830:0.485720:0.399830:0.485720:0.383361:0.407618:0.383361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Particularmente, si   = 1, obtenemos::@0.108236:0.434416:0.370627:0.434416:0.370627:0.417918:0.108236:0.417918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.242862:0.434531:0.251840:0.434531:0.251840:0.418063:0.242862:0.418063:0.000000
S:@0.167670:0.462567:0.175549:0.462567:0.175549:0.446099:0.167670:0.446099:0.000000
n:@0.175470:0.465804:0.180929:0.465804:0.180929:0.456203:0.175470:0.456203:0.000000
 = 1 + :@0.180928:0.462459:0.227608:0.462459:0.227608:0.445961:0.180928:0.445961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d + d:@0.227608:0.462574:0.265118:0.462574:0.265118:0.446105:0.227608:0.446105:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.265118:0.456107:0.270071:0.456107:0.270071:0.446489:0.265118:0.446489:0.000000
 + … +   =        =                 , si   ≠ 1:@0.270070:0.462459:0.533484:0.462459:0.533484:0.445961:0.270070:0.445961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.323299:0.462574:0.332470:0.462574:0.332470:0.446105:0.323299:0.446105:0.000000
n:@0.332469:0.456107:0.338085:0.456107:0.338085:0.446489:0.332469:0.446489:0.000000
d:@0.377886:0.462574:0.387057:0.462574:0.387057:0.446105:0.377886:0.446105:0.000000
j:@0.388020:0.456174:0.390266:0.456174:0.390266:0.446573:0.388020:0.446573:0.000000
d:@0.496726:0.462574:0.505896:0.462574:0.505896:0.446105:0.496726:0.446105:0.000000
.:@0.533484:0.462574:0.536336:0.462574:0.536336:0.446105:0.533484:0.446105:0.000000
Ejercicios resueltos:@0.108242:0.504664:0.238897:0.504664:0.238897:0.487877:0.108242:0.487877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108242:0.521856:0.120514:0.521856:0.120514:0.505141:0.108242:0.505141:0.000000:0.000000
  De una progresión geométrica ( ) se conocen los términos:@0.120514:0.521640:0.553885:0.521638:0.553885:0.505141:0.120514:0.505142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.358129:0.521755:0.365565:0.521755:0.365565:0.505287:0.358129:0.505287:0.000000
n:@0.365699:0.524984:0.371158:0.524984:0.371158:0.515383:0.365699:0.515383:0.000000
 :@0.108224:0.546118:0.112366:0.546118:0.112366:0.529620:0.108224:0.529620:0.000000
g:@0.131959:0.546234:0.139396:0.546234:0.139396:0.529765:0.131959:0.529765:0.000000
2:@0.139413:0.549395:0.144366:0.549395:0.144366:0.539777:0.139413:0.539777:0.000000
 =      , y   =          .:@0.144366:0.546118:0.274542:0.546118:0.274542:0.529620:0.144366:0.529620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.203029:0.546234:0.210465:0.546234:0.210465:0.529765:0.203029:0.529765:0.000000
5:@0.210463:0.549395:0.215416:0.549395:0.215416:0.539777:0.210463:0.539777:0.000000
 :@0.108225:0.570597:0.112367:0.570597:0.112367:0.554099:0.108225:0.554099:0.000000
Obtén el término general de esta progresión, así como la suma de :@0.131959:0.570597:0.599891:0.570597:0.599891:0.554099:0.131959:0.554099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los   primeros términos.:@0.131959:0.587947:0.303515:0.587947:0.303515:0.571450:0.131959:0.571450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.155810:0.588063:0.165173:0.588063:0.165173:0.571594:0.155810:0.571594:0.000000
 :@0.108225:0.622649:0.112367:0.622649:0.112367:0.606151:0.108225:0.606151:0.000000
Se ha visto que el término general de una progresión geométrica :@0.131959:0.622649:0.599872:0.622649:0.599872:0.606151:0.131959:0.606151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) está definido como    = :@0.131959:0.640000:0.336140:0.640000:0.336140:0.623502:0.131959:0.623502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.137912:0.640115:0.145349:0.640115:0.145349:0.623646:0.137912:0.623646:0.000000
n:@0.145500:0.643345:0.150959:0.643345:0.150959:0.633744:0.145500:0.633744:0.000000
g:@0.304557:0.640115:0.311994:0.640115:0.311994:0.623646:0.304557:0.623646:0.000000
n:@0.312150:0.643345:0.317609:0.643345:0.317609:0.633744:0.312150:0.633744:0.000000
ad n:@0.335524:0.640115:0.374667:0.640115:0.374667:0.623646:0.335524:0.623646:0.000000:0.000000:0.000000:0.000000
n:@0.353565:0.633715:0.359024:0.633715:0.359024:0.624114:0.353565:0.624114:0.000000
,      . Con la información dada, :@0.359023:0.640000:0.599889:0.640000:0.599889:0.623502:0.359023:0.623502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.378394:0.639481:0.393046:0.639481:0.393046:0.626108:0.378394:0.626108:0.000000
N:@0.396756:0.639031:0.411745:0.639031:0.411745:0.625584:0.396756:0.625584:0.000000
obtenemos las constantes   y  . Tenemos el siguiente par de ecua-:@0.131975:0.657350:0.595682:0.657350:0.595682:0.640853:0.131975:0.640853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a d:@0.318784:0.657466:0.351920:0.657466:0.351920:0.640997:0.318784:0.640997:0.000000:0.000000:0.000000
ciones::@0.131975:0.674701:0.180330:0.674701:0.180330:0.658203:0.131975:0.658203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108239:0.699181:0.112381:0.699181:0.112381:0.682683:0.108239:0.682683:0.000000
g:@0.256428:0.699296:0.263864:0.699296:0.263864:0.682828:0.256428:0.682828:0.000000
2:@0.263854:0.702457:0.268808:0.702457:0.268808:0.692839:0.263854:0.692839:0.000000
 =      = :@0.268808:0.699179:0.323560:0.699179:0.323560:0.682682:0.268808:0.682682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad:@0.323560:0.699295:0.341669:0.699295:0.341669:0.682826:0.323560:0.682826:0.000000:0.000000
2:@0.341668:0.692828:0.346621:0.692828:0.346621:0.683210:0.341668:0.683210:0.000000
,     =          = :@0.346621:0.699179:0.445511:0.699179:0.445511:0.682682:0.346621:0.682682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.361802:0.699295:0.369239:0.699295:0.369239:0.682826:0.361802:0.682826:0.000000
5:@0.369237:0.702457:0.374190:0.702457:0.374190:0.692839:0.369237:0.692839:0.000000
ad:@0.445511:0.699295:0.463620:0.699295:0.463620:0.682826:0.445511:0.682826:0.000000:0.000000
5:@0.463618:0.692828:0.468572:0.692828:0.468572:0.683210:0.463618:0.683210:0.000000
.:@0.468570:0.699179:0.471325:0.699179:0.471325:0.682682:0.468570:0.682682:0.000000
 :@0.108234:0.737438:0.112376:0.737438:0.112376:0.720940:0.108234:0.720940:0.000000
De la primera ecuación se obtiene   =        ,  y se reemplaza en:@0.131968:0.737438:0.572098:0.737438:0.572098:0.720940:0.131968:0.720940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.378232:0.737554:0.387209:0.737554:0.387209:0.721085:0.378232:0.721085:0.000000
 :@0.108234:0.769045:0.112376:0.769045:0.112376:0.752547:0.108234:0.752547:0.000000
la segunda ecuación,         =           =       ,       :@0.131968:0.769045:0.463704:0.769053:0.463704:0.752555:0.131968:0.752547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.363900:0.769161:0.373071:0.769161:0.373071:0.752692:0.363900:0.752692:0.000000
5:@0.373077:0.762700:0.378030:0.762700:0.378030:0.753082:0.373077:0.753082:0.000000
d:@0.417832:0.769168:0.427003:0.769168:0.427003:0.752700:0.417832:0.752700:0.000000
3:@0.427001:0.762700:0.431954:0.762700:0.431954:0.753082:0.427001:0.753082:0.000000
 :@0.108241:0.800660:0.112383:0.800660:0.112383:0.784162:0.108241:0.784162:0.000000
de donde   =       , y en consecuencia,   =      . Calculamos  : :@0.131976:0.800660:0.565325:0.800659:0.565325:0.784161:0.131976:0.784162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.205011:0.800776:0.214181:0.800776:0.214181:0.784307:0.205011:0.784307:0.000000
3:@0.214180:0.794307:0.219133:0.794307:0.219133:0.784689:0.214180:0.784689:0.000000
d:@0.406832:0.800774:0.416002:0.800774:0.416002:0.784306:0.406832:0.784306:0.000000
a:@0.549450:0.800774:0.558428:0.800774:0.558428:0.784306:0.549450:0.784306:0.000000
a:@0.271938:0.839033:0.280916:0.839033:0.280916:0.822564:0.271938:0.822564:0.000000
 =         =             =     .:@0.280916:0.838917:0.432071:0.838917:0.432071:0.822419:0.280916:0.822419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108242:0.887875:0.112384:0.887875:0.112384:0.871377:0.108242:0.871377:0.000000
Así, el término general de la progresión geométrica está dado:@0.131976:0.887875:0.565573:0.887875:0.565573:0.871377:0.131976:0.871377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como  =            , …      .:@0.131976:0.915911:0.332090:0.915925:0.332090:0.899427:0.131976:0.899414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.177905:0.916027:0.185341:0.916027:0.185341:0.899558:0.177905:0.899558:0.000000
n:@0.185380:0.919269:0.190838:0.919269:0.190838:0.909668:0.185380:0.909668:0.000000
n:@0.281577:0.916040:0.290940:0.916040:0.290940:0.899572:0.281577:0.899572:0.000000
:@0.295272:0.915406:0.309924:0.915406:0.309924:0.902033:0.295272:0.902033:0.000000
N:@0.314251:0.914956:0.329239:0.914956:0.329239:0.901509:0.314251:0.901509:0.000000
 :@0.108229:0.940404:0.112371:0.940404:0.112371:0.923906:0.108229:0.923906:0.000000
Nota que esta sucesión es estrictamente creciente.:@0.131963:0.940404:0.489888:0.940404:0.489888:0.923906:0.131963:0.923906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∑:@0.468106:0.205317:0.483485:0.205317:0.483485:0.179495:0.468106:0.179495:0.000000
n:@0.473541:0.185950:0.478999:0.185950:0.478999:0.176349:0.473541:0.176349:0.000000
k:@0.468240:0.211011:0.473047:0.211011:0.473047:0.201410:0.468240:0.201410:0.000000
=0:@0.473047:0.210944:0.484301:0.210944:0.484301:0.201326:0.473047:0.201326:0.000000:0.000000
∑:@0.263752:0.403474:0.279131:0.403474:0.279131:0.377652:0.263752:0.377652:0.000000
n:@0.269187:0.384107:0.274645:0.384107:0.274645:0.374506:0.269187:0.374506:0.000000
k:@0.263885:0.409168:0.268693:0.409168:0.268693:0.399567:0.263885:0.399567:0.000000
=0:@0.268693:0.409101:0.279947:0.409101:0.279947:0.399483:0.268693:0.399483:0.000000:0.000000
∑:@0.359241:0.466695:0.374620:0.466695:0.374620:0.440873:0.359241:0.440873:0.000000
n:@0.364675:0.447329:0.370134:0.447329:0.370134:0.437728:0.364675:0.437728:0.000000
j:@0.360654:0.472390:0.362901:0.472390:0.362901:0.462789:0.360654:0.462789:0.000000
=0:@0.362901:0.472323:0.374155:0.472323:0.374155:0.462705:0.362901:0.462705:0.000000:0.000000
d:@0.330098:0.392398:0.339269:0.392398:0.339269:0.375929:0.330098:0.375929:0.000000
n:@0.339192:0.385997:0.344650:0.385997:0.344650:0.376396:0.339192:0.376396:0.000000
+1:@0.344650:0.385929:0.355904:0.385929:0.355904:0.376311:0.344650:0.376311:0.000000:0.000000
 – 1 :@0.355904:0.392282:0.387325:0.392282:0.387325:0.375785:0.355904:0.375785:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.338411:0.408737:0.347581:0.408737:0.347581:0.392268:0.338411:0.392268:0.000000
 – 1:@0.347581:0.408621:0.374861:0.408621:0.374861:0.392123:0.347581:0.392123:0.000000:0.000000:0.000000:0.000000
d:@0.413860:0.455619:0.423031:0.455619:0.423031:0.439150:0.413860:0.439150:0.000000
n:@0.422954:0.449219:0.428412:0.449219:0.428412:0.439618:0.422954:0.439618:0.000000
+1:@0.428412:0.449151:0.439666:0.449151:0.439666:0.439533:0.428412:0.439533:0.000000:0.000000
 – 1 :@0.439666:0.455503:0.471087:0.455503:0.471087:0.439006:0.439666:0.439006:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.422173:0.471957:0.431343:0.471957:0.431343:0.455489:0.422173:0.455489:0.000000
 – 1:@0.431343:0.471842:0.458623:0.471842:0.458623:0.455344:0.431343:0.455344:0.000000:0.000000:0.000000:0.000000
1 – :@0.422567:0.392282:0.449846:0.392282:0.449846:0.375785:0.422567:0.375785:0.000000:0.000000:0.000000:0.000000
d:@0.449846:0.392398:0.459017:0.392398:0.459017:0.375929:0.449846:0.375929:0.000000
n:@0.458939:0.385997:0.464398:0.385997:0.464398:0.376396:0.458939:0.376396:0.000000
+1:@0.464398:0.385929:0.475652:0.385929:0.475652:0.376311:0.464398:0.376311:0.000000:0.000000
 :@0.475652:0.392282:0.479794:0.392282:0.479794:0.375785:0.475652:0.375785:0.000000
1 – :@0.430879:0.408621:0.458159:0.408621:0.458159:0.392123:0.430879:0.392123:0.000000:0.000000:0.000000:0.000000
d:@0.458159:0.408737:0.467329:0.408737:0.467329:0.392268:0.458159:0.392268:0.000000
9:@0.169172:0.538664:0.177668:0.538664:0.177668:0.522166:0.169172:0.522166:0.000000
8:@0.169172:0.555002:0.177668:0.555002:0.177668:0.538505:0.169172:0.538505:0.000000
9:@0.292178:0.691740:0.300674:0.691740:0.300674:0.675242:0.292178:0.675242:0.000000
8:@0.292178:0.708079:0.300674:0.708079:0.300674:0.691581:0.292178:0.691581:0.000000
9:@0.415221:0.729697:0.423717:0.729697:0.423717:0.713199:0.415221:0.713199:0.000000
8:@0.408150:0.746035:0.416646:0.746035:0.416646:0.729538:0.408150:0.729538:0.000000
d:@0.416743:0.746151:0.425913:0.746151:0.425913:0.729682:0.416743:0.729682:0.000000
2:@0.425922:0.739689:0.430875:0.739689:0.430875:0.730070:0.425922:0.730070:0.000000
9:@0.343582:0.761594:0.352078:0.761594:0.352078:0.745097:0.343582:0.745097:0.000000
8:@0.336512:0.777933:0.345008:0.777933:0.345008:0.761435:0.336512:0.761435:0.000000
d:@0.345104:0.778049:0.354275:0.778049:0.354275:0.761580:0.345104:0.761580:0.000000
2:@0.354282:0.771586:0.359235:0.771586:0.359235:0.761968:0.354282:0.761968:0.000000
9:@0.309813:0.831715:0.318309:0.831715:0.318309:0.815218:0.309813:0.815218:0.000000
8:@0.302743:0.848054:0.311239:0.848054:0.311239:0.831556:0.302743:0.831556:0.000000
d:@0.311335:0.848170:0.320505:0.848170:0.320505:0.831701:0.311335:0.831701:0.000000
2:@0.320514:0.841708:0.325468:0.841708:0.325468:0.832090:0.320514:0.832090:0.000000
9:@0.367656:0.831715:0.376152:0.831715:0.376152:0.815218:0.367656:0.815218:0.000000
8:@0.350625:0.858117:0.359121:0.858117:0.359121:0.841620:0.350625:0.841620:0.000000
3:@0.368487:0.850506:0.376983:0.850506:0.376983:0.834008:0.368487:0.834008:0.000000
2:@0.368487:0.866844:0.376983:0.866844:0.376983:0.850347:0.368487:0.850347:0.000000
3:@0.237818:0.908134:0.246314:0.908134:0.246314:0.891636:0.237818:0.891636:0.000000
2:@0.237818:0.924473:0.246314:0.924473:0.246314:0.907975:0.237818:0.907975:0.000000
1:@0.215184:0.908134:0.223680:0.908134:0.223680:0.891636:0.215184:0.891636:0.000000
2:@0.215184:0.924473:0.223680:0.924473:0.223680:0.907975:0.215184:0.907975:0.000000
9:@0.402228:0.761594:0.410724:0.761594:0.410724:0.745097:0.402228:0.745097:0.000000
8:@0.402228:0.777933:0.410724:0.777933:0.410724:0.761435:0.402228:0.761435:0.000000
27:@0.240478:0.793314:0.257663:0.793314:0.257663:0.776816:0.240478:0.776816:0.000000:0.000000
8:@0.244813:0.809652:0.253309:0.809652:0.253309:0.793154:0.244813:0.793154:0.000000
3:@0.440430:0.793314:0.448926:0.793314:0.448926:0.776816:0.440430:0.776816:0.000000
2:@0.440430:0.809652:0.448926:0.809652:0.448926:0.793154:0.440430:0.793154:0.000000
1:@0.415353:0.831715:0.423849:0.831715:0.423849:0.815218:0.415353:0.815218:0.000000
2:@0.415353:0.848054:0.423849:0.848054:0.423849:0.831556:0.415353:0.831556:0.000000
243:@0.285204:0.761594:0.311077:0.761594:0.311077:0.745097:0.285204:0.745097:0.000000:0.000000:0.000000
64:@0.289538:0.777933:0.306723:0.777933:0.306723:0.761435:0.289538:0.761435:0.000000:0.000000
243:@0.397510:0.691740:0.423383:0.691740:0.423383:0.675242:0.397510:0.675242:0.000000:0.000000:0.000000
64:@0.401864:0.708079:0.419049:0.708079:0.419049:0.691581:0.401864:0.691581:0.000000:0.000000
243:@0.238349:0.538664:0.264222:0.538664:0.264222:0.522166:0.238349:0.522166:0.000000:0.000000:0.000000
64:@0.242684:0.555002:0.259868:0.555002:0.259868:0.538505:0.242684:0.538505:0.000000:0.000000
2:@0.384830:0.843372:0.389332:0.843372:0.389332:0.834188:0.384830:0.834188:0.000000
n:@0.252849:0.898483:0.258070:0.898483:0.258070:0.889299:0.252849:0.889299:0.000000
Competencia :@0.684804:0.213142:0.782426:0.213142:0.782426:0.197670:0.684804:0.197670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.684804:0.225710:0.796762:0.225710:0.796762:0.210238:0.684804:0.210238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otras formas de escribir :@0.678232:0.250185:0.837419:0.250185:0.837419:0.235122:0.678232:0.235122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los términos de una progresión :@0.638496:0.266027:0.843910:0.266027:0.843910:0.250964:0.638496:0.250964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
geométrica son::@0.638496:0.281869:0.741448:0.281869:0.741448:0.266806:0.638496:0.266806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Razón:@0.638496:0.305262:0.682082:0.305262:0.682082:0.289790:0.638496:0.289790:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.682084:0.305038:0.685145:0.305038:0.685145:0.289776:0.682084:0.289776:0.000000
Si la razón es r > 1, la progre-:@0.638496:0.320682:0.823594:0.320682:0.823594:0.305618:0.638496:0.305618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sión es creciente, y decreciente :@0.638496:0.336524:0.841764:0.336524:0.841764:0.321460:0.638496:0.321460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando 0 < r < 1.:@0.638496:0.352366:0.749788:0.352366:0.749788:0.337302:0.638496:0.337302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Se calcula dividiendo un tér-:@0.638496:0.368208:0.838617:0.368208:0.838617:0.353144:0.638496:0.353144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mino por el que le precede.:@0.655118:0.384050:0.832897:0.384050:0.832897:0.368986:0.655118:0.368986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  La razón puede ser un núme-:@0.638496:0.399891:0.846512:0.399891:0.846512:0.384828:0.638496:0.384828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ro positivo o negativo.:@0.655118:0.415733:0.798984:0.415733:0.798984:0.400670:0.655118:0.400670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Notación y término n-ésimo:@0.638496:0.439127:0.836380:0.439127:0.836380:0.423654:0.638496:0.423654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.836380:0.438902:0.839441:0.438902:0.839441:0.423641:0.836380:0.423641:0.000000
  a:@0.638495:0.454652:0.663315:0.454652:0.663315:0.439615:0.638495:0.439615:0.000000:0.000000:0.000000
 = primer término;   = razón :@0.663315:0.454546:0.850364:0.454546:0.850364:0.439483:0.663315:0.439483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.787007:0.454652:0.792512:0.454652:0.792512:0.439615:0.787007:0.439615:0.000000
o diferencia;    = número de :@0.655118:0.470388:0.842276:0.470388:0.842276:0.455325:0.655118:0.455325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.740377:0.470494:0.748926:0.470494:0.748926:0.455457:0.740377:0.455457:0.000000
términos:@0.655118:0.486230:0.713359:0.486230:0.713359:0.471167:0.655118:0.471167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  Término n-ésimo :@0.638495:0.502072:0.763647:0.502072:0.763647:0.487009:0.638495:0.487009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un:@0.763207:0.502178:0.782117:0.502178:0.782117:0.487141:0.763207:0.487141:0.000000:0.000000
 = a • :@0.781679:0.502072:0.816067:0.502072:0.816067:0.487009:0.781679:0.487009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r :@0.815627:0.502178:0.824475:0.502178:0.824475:0.487141:0.815627:0.487141:0.000000:0.000000
n – :@0.824040:0.496332:0.838007:0.496332:0.838007:0.487566:0.824040:0.487566:0.000000:0.000000:0.000000:0.000000
1:@0.837750:0.496271:0.842273:0.496271:0.842273:0.487489:0.837750:0.487489:0.000000
, :@0.842015:0.502070:0.848312:0.502070:0.848312:0.487007:0.842015:0.487007:0.000000:0.000000
el último término:   = :@0.655121:0.517912:0.796562:0.517912:0.796562:0.502849:0.655121:0.502849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l ar :@0.775665:0.518017:0.813906:0.518017:0.813906:0.502981:0.775665:0.502981:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.813908:0.512174:0.818892:0.512174:0.818892:0.503408:0.813908:0.503408:0.000000
–1:@0.818892:0.512113:0.829003:0.512113:0.829003:0.503331:0.818892:0.503331:0.000000:0.000000
Suma de los primeros  :@0.638503:0.541305:0.796634:0.541305:0.796634:0.525833:0.638503:0.525833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
términos:@0.638503:0.557147:0.701984:0.557147:0.701984:0.541675:0.638503:0.541675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.701984:0.556923:0.705045:0.556923:0.705045:0.541662:0.701984:0.541662:0.000000
= ⋅:@0.657633:0.585500:0.684351:0.585500:0.684351:0.571484:0.657633:0.571484:0.000000:0.000000:0.000000
⎛:@0.685573:0.576836:0.691941:0.576836:0.691941:0.562820:0.685573:0.562820:0.000000
⎝:@0.685573:0.595224:0.691941:0.595224:0.691941:0.581208:0.685573:0.581208:0.000000
⎜:@0.685573:0.589996:0.691941:0.589996:0.691941:0.575981:0.685573:0.575981:0.000000
⎞:@0.727507:0.576836:0.733876:0.576836:0.733876:0.562820:0.727507:0.562820:0.000000
⎠:@0.727507:0.595224:0.733876:0.595224:0.733876:0.581208:0.727507:0.581208:0.000000
⎟:@0.727507:0.589996:0.733876:0.589996:0.733876:0.575981:0.727507:0.575981:0.000000
=:@0.756663:0.585503:0.765768:0.585503:0.765768:0.571487:0.756663:0.571487:0.000000
–1:@0.710874:0.576827:0.728487:0.576827:0.728487:0.562077:0.710874:0.562077:0.000000:0.000000
–1:@0.707388:0.594332:0.725001:0.594332:0.725001:0.579582:0.707388:0.579582:0.000000:0.000000
;:@0.737124:0.584897:0.740010:0.584897:0.740010:0.570147:0.737124:0.570147:0.000000
,:@0.741552:0.584897:0.744438:0.584897:0.744438:0.570147:0.741552:0.570147:0.000000
–:@0.781311:0.576828:0.789603:0.576828:0.789603:0.562078:0.781311:0.562078:0.000000
–1:@0.782159:0.594334:0.799772:0.594334:0.799772:0.579584:0.782159:0.579584:0.000000:0.000000
S:@0.641187:0.584899:0.648451:0.584899:0.648451:0.570174:0.641187:0.570174:0.000000
a:@0.670028:0.584899:0.678370:0.584899:0.678370:0.570174:0.670028:0.570174:0.000000
r:@0.695795:0.576830:0.700555:0.576830:0.700555:0.562104:0.695795:0.562104:0.000000
r:@0.699234:0.594335:0.703994:0.594335:0.703994:0.579610:0.699234:0.579610:0.000000
S:@0.745970:0.584900:0.753235:0.584900:0.753235:0.570175:0.745970:0.570175:0.000000
lr a:@0.770050:0.576831:0.800536:0.576831:0.800536:0.562106:0.770050:0.562106:0.000000:0.000000:0.000000:0.000000
r:@0.774007:0.594336:0.778767:0.594336:0.778767:0.579611:0.774007:0.579611:0.000000
n:@0.648397:0.586694:0.653357:0.586694:0.653357:0.578160:0.648397:0.578160:0.000000
n:@0.702111:0.569931:0.707070:0.569931:0.707070:0.561397:0.702111:0.561397:0.000000
Aplicación de progresiones :@0.638503:0.616757:0.831830:0.616757:0.831830:0.601285:0.638503:0.601285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en finanzas: Valor futuro:@0.638503:0.632599:0.811058:0.632599:0.811058:0.617127:0.638503:0.617127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.811058:0.632375:0.814119:0.632375:0.814119:0.617114:0.811058:0.617114:0.000000
( ):@0.755227:0.660352:0.785311:0.660352:0.785311:0.642412:0.755227:0.642412:0.000000:0.000000:0.000000
( ):@0.812123:0.660352:0.842207:0.660352:0.842207:0.642412:0.812123:0.642412:0.000000:0.000000:0.000000
=:@0.659492:0.658143:0.667368:0.658143:0.667368:0.644127:0.659492:0.644127:0.000000
+:@0.694539:0.658143:0.702415:0.658143:0.702415:0.644127:0.694539:0.644127:0.000000
=:@0.720663:0.658143:0.728539:0.658143:0.728539:0.644127:0.720663:0.644127:0.000000
+ =:@0.765451:0.658143:0.795262:0.658143:0.795262:0.644127:0.765451:0.644127:0.000000:0.000000:0.000000
+:@0.822362:0.658143:0.830238:0.658143:0.830238:0.644127:0.822362:0.644127:0.000000
VF VF:@0.639939:0.657533:0.681872:0.657533:0.681872:0.643679:0.639939:0.643679:0.000000:0.000000:0.000000:0.000000:0.000000
VF:@0.729931:0.657533:0.743043:0.657533:0.743043:0.643679:0.729931:0.643679:0.000000:0.000000
r:@0.775207:0.657533:0.779324:0.657533:0.779324:0.643679:0.775207:0.643679:0.000000
VP:@0.796639:0.657533:0.810325:0.657533:0.810325:0.643679:0.796639:0.643679:0.000000:0.000000
r:@0.832102:0.657533:0.836220:0.657533:0.836220:0.643679:0.832102:0.643679:0.000000
n:@0.651790:0.659337:0.656080:0.659337:0.656080:0.651308:0.651790:0.651308:0.000000
n:@0.680606:0.659337:0.684896:0.659337:0.684896:0.651308:0.680606:0.651308:0.000000
n:@0.741781:0.659337:0.746071:0.659337:0.746071:0.651308:0.741781:0.651308:0.000000
n:@0.842572:0.648942:0.846862:0.648942:0.846862:0.640913:0.842572:0.640913:0.000000
int:@0.703672:0.657533:0.718534:0.657533:0.718534:0.643430:0.703672:0.643430:0.000000:0.000000:0.000000
1:@0.759334:0.657533:0.766335:0.657533:0.766335:0.643430:0.759334:0.643430:0.000000
1:@0.816230:0.657533:0.823231:0.657533:0.823231:0.643430:0.816230:0.643430:0.000000
–1:@0.685047:0.659337:0.693020:0.659337:0.693020:0.651163:0.685047:0.651163:0.000000:0.000000
–1:@0.746221:0.659337:0.754194:0.659337:0.754194:0.651163:0.746221:0.651163:0.000000:0.000000
(:@0.672192:0.699728:0.677715:0.699728:0.677715:0.681788:0.672192:0.681788:0.000000
):@0.701448:0.699728:0.706971:0.699728:0.706971:0.681788:0.701448:0.681788:0.000000
=:@0.659471:0.686381:0.668576:0.686381:0.668576:0.672365:0.659471:0.672365:0.000000
+:@0.684016:0.697521:0.693121:0.697521:0.693121:0.683506:0.684016:0.683506:0.000000
VP:@0.640149:0.685771:0.655955:0.685771:0.655955:0.671917:0.640149:0.671917:0.000000:0.000000
VF:@0.682607:0.678103:0.697765:0.678103:0.697765:0.664250:0.682607:0.664250:0.000000:0.000000
r:@0.695277:0.696911:0.700037:0.696911:0.700037:0.683057:0.695277:0.683057:0.000000
n:@0.696316:0.679901:0.701276:0.679901:0.701276:0.671872:0.696316:0.671872:0.000000
n:@0.707389:0.688319:0.712348:0.688319:0.712348:0.680291:0.707389:0.680291:0.000000
1:@0.676950:0.696909:0.685044:0.696909:0.685044:0.682807:0.676950:0.682807:0.000000
Donde::@0.638503:0.719072:0.686295:0.719072:0.686295:0.704009:0.638503:0.704009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.660848:0.735585:0.669953:0.735585:0.669953:0.721570:0.660848:0.721570:0.000000
=:@0.660471:0.754256:0.669576:0.754256:0.669576:0.740241:0.660471:0.740241:0.000000
Valor presente o actual:@0.673569:0.734975:0.826217:0.734975:0.826217:0.720873:0.673569:0.720873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
..:@0.705993:0.734975:0.711615:0.734975:0.711615:0.720873:0.705993:0.720873:0.000000:0.000000
.. ..:@0.768236:0.734975:0.787955:0.734975:0.787955:0.720873:0.768236:0.720873:0.000000:0.000000:0.000000:0.000000:0.000000
Valor final o futuro:@0.673193:0.753646:0.797364:0.753646:0.797364:0.739544:0.673193:0.739544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
..:@0.705616:0.753646:0.711238:0.753646:0.711238:0.739544:0.705616:0.739544:0.000000:0.000000
.. ..:@0.737990:0.753646:0.757709:0.753646:0.757709:0.739544:0.737990:0.739544:0.000000:0.000000:0.000000:0.000000:0.000000
VP:@0.641201:0.734975:0.657006:0.734975:0.657006:0.721122:0.641201:0.721122:0.000000:0.000000
VF:@0.641201:0.753646:0.656359:0.753646:0.656359:0.739793:0.641201:0.739793:0.000000:0.000000
Define:@0.638503:0.777894:0.684816:0.777894:0.684816:0.762422:0.638503:0.762422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 con tus palabras qué es :@0.684816:0.777472:0.843353:0.777472:0.843353:0.762408:0.684816:0.762408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una progresión geométrica.:@0.638503:0.793314:0.816143:0.793314:0.816143:0.778250:0.638503:0.778250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000