115:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000 Interdisciplinariedad:@0.684804:0.109928:0.831589:0.109928:0.831589:0.094455:0.684804:0.094455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática y Biología :@0.685042:0.138979:0.845250:0.138979:0.845250:0.123507:0.685042:0.123507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El estudio de sucesiones es am-:@0.638498:0.154398:0.840481:0.154398:0.840481:0.139335:0.638498:0.139335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pliamente utilizado en biología :@0.638498:0.170240:0.842645:0.170240:0.842645:0.155177:0.638498:0.155177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para analizar la reproducción :@0.638498:0.186082:0.829454:0.186082:0.829454:0.171019:0.638498:0.171019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 bacteriana, considerando que :@0.638498:0.201924:0.833605:0.201924:0.833605:0.186861:0.638498:0.186861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una bacteria se reproduce por :@0.638498:0.217766:0.837156:0.217766:0.837156:0.202703:0.638498:0.202703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 bipartición. En condiciones :@0.638498:0.233608:0.817758:0.233608:0.817758:0.218545:0.638498:0.218545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 muy favorables, la población de :@0.638498:0.249450:0.847271:0.249450:0.847271:0.234387:0.638498:0.234387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 algunas bacterias puede llegar :@0.638498:0.265292:0.835732:0.265292:0.835732:0.250229:0.638498:0.250229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a doblarse cada 15 minutos, :@0.638498:0.281134:0.823332:0.281134:0.823332:0.266071:0.638498:0.266071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 duplicaciones por hora y 96 :@0.638498:0.296976:0.834237:0.296976:0.834237:0.281913:0.638498:0.281913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diarias. Por ello, el análisis del :@0.638498:0.312818:0.826692:0.312818:0.826692:0.297755:0.638498:0.297755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 comportamiento de reproduc-:@0.638498:0.328660:0.838356:0.328660:0.838356:0.313597:0.638498:0.313597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ción es importante para contro-:@0.638498:0.344502:0.846657:0.344502:0.846657:0.329439:0.638498:0.329439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lar su expansión.:@0.638498:0.360344:0.744654:0.360344:0.744654:0.345281:0.638498:0.345281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Indaga escribe:@0.638498:0.383738:0.750631:0.383738:0.750631:0.368265:0.638498:0.368265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.686130:0.383315:0.700836:0.383315:0.700836:0.368252:0.686130:0.368252:0.000000:0.000000:0.000000 otras aplica-:@0.750635:0.383315:0.833236:0.383315:0.833236:0.368252:0.750635:0.368252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ciones de las sucesiones numéri-:@0.638498:0.399157:0.845973:0.399157:0.845973:0.384094:0.638498:0.384094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ca en la vida diaria.:@0.638498:0.414999:0.759744:0.414999:0.759744:0.399936:0.638498:0.399936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.638503:0.546686:0.649984:0.546686:0.649984:0.536661:0.638503:0.536661:0.000000 :@0.649984:0.547394:0.652865:0.547394:0.652865:0.535917:0.649984:0.535917:0.000000 Biofilm de bacterias:@0.652865:0.547394:0.750014:0.547394:0.750014:0.535917:0.652865:0.535917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Shutterstock, 367715540:@0.871305:0.528513:0.871305:0.460339:0.859836:0.460339:0.859836:0.528513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicio resuelto:@0.108233:0.107262:0.226211:0.107262:0.226211:0.090475:0.108233:0.090475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dado :@0.108233:0.124237:0.151424:0.124237:0.151424:0.107739:0.108233:0.107739:0.000000:0.000000:0.000000:0.000000:0.000000 α :@0.151290:0.131823:0.165922:0.131823:0.165922:0.112824:0.151290:0.112824:0.000000:0.000000 :@0.165930:0.124020:0.181978:0.124020:0.181978:0.109373:0.165930:0.109373:0.000000 constante no nula, la sucesión definida:@0.182363:0.124237:0.474259:0.124237:0.474259:0.107739:0.182363:0.107739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.186891:0.123150:0.200195:0.123150:0.200195:0.110288:0.186891:0.110288:0.000000 como :@0.108241:0.152273:0.337960:0.152273:0.337960:0.135775:0.108241:0.135775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cinco de sus términos se describen a continuación::@0.108241:0.183880:0.461853:0.183880:0.461853:0.167383:0.108241:0.167383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.108241:0.201347:0.117218:0.201347:0.117218:0.184878:0.108241:0.184878:0.000000 1:@0.117076:0.204515:0.122029:0.204515:0.122029:0.194896:0.117076:0.194896:0.000000 = :@0.121950:0.201238:0.140772:0.201238:0.140772:0.184740:0.121950:0.184740:0.000000:0.000000:0.000000 α:@0.140637:0.208824:0.151215:0.208824:0.151215:0.189825:0.140637:0.189825:0.000000 a:@0.151587:0.201354:0.160564:0.201354:0.160564:0.184885:0.151587:0.184885:0.000000 0:@0.160430:0.204515:0.165383:0.204515:0.165383:0.194896:0.160430:0.194896:0.000000 , = :@0.165303:0.201238:0.216491:0.201238:0.216491:0.184740:0.165303:0.184740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.183952:0.201354:0.192930:0.201354:0.192930:0.184885:0.183952:0.184885:0.000000 2:@0.192794:0.204515:0.197747:0.204515:0.197747:0.194896:0.192794:0.194896:0.000000 α:@0.216356:0.208824:0.226934:0.208824:0.226934:0.189825:0.216356:0.189825:0.000000 a:@0.227306:0.201354:0.236283:0.201354:0.236283:0.184885:0.227306:0.184885:0.000000 1:@0.236149:0.204515:0.241103:0.204515:0.241103:0.194896:0.236149:0.194896:0.000000 = :@0.241023:0.201238:0.259845:0.201238:0.259845:0.184740:0.241023:0.184740:0.000000:0.000000:0.000000 a:@0.259710:0.201354:0.268688:0.201354:0.268688:0.184885:0.259710:0.184885:0.000000 0:@0.268553:0.204515:0.273507:0.204515:0.273507:0.194896:0.268553:0.194896:0.000000 α:@0.273427:0.208824:0.284004:0.208824:0.284004:0.189825:0.273427:0.189825:0.000000 2:@0.284378:0.194885:0.289331:0.194885:0.289331:0.185267:0.284378:0.185267:0.000000 , = :@0.289251:0.201238:0.336432:0.201238:0.336432:0.184740:0.289251:0.184740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.303893:0.201354:0.312870:0.201354:0.312870:0.184885:0.303893:0.184885:0.000000 3:@0.312735:0.204515:0.317688:0.204515:0.317688:0.194896:0.312735:0.194896:0.000000 α:@0.336297:0.208824:0.346874:0.208824:0.346874:0.189825:0.336297:0.189825:0.000000 a:@0.347246:0.201354:0.356224:0.201354:0.356224:0.184885:0.347246:0.184885:0.000000 2:@0.356090:0.204515:0.361043:0.204515:0.361043:0.194896:0.356090:0.194896:0.000000 = :@0.360963:0.201238:0.379785:0.201238:0.379785:0.184740:0.360963:0.184740:0.000000:0.000000:0.000000 a:@0.379650:0.201354:0.388628:0.201354:0.388628:0.184885:0.379650:0.184885:0.000000 0:@0.388494:0.204515:0.393447:0.204515:0.393447:0.194896:0.388494:0.194896:0.000000 α:@0.393367:0.208824:0.403945:0.208824:0.403945:0.189825:0.393367:0.189825:0.000000 3 :@0.404318:0.194885:0.411608:0.194885:0.411608:0.185267:0.404318:0.185267:0.000000:0.000000 , = :@0.411528:0.201238:0.458709:0.201238:0.458709:0.184740:0.411528:0.184740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.426170:0.201354:0.435148:0.201354:0.435148:0.184885:0.426170:0.184885:0.000000 4:@0.435012:0.204515:0.439965:0.204515:0.439965:0.194896:0.435012:0.194896:0.000000 α:@0.458573:0.208824:0.469150:0.208824:0.469150:0.189825:0.458573:0.189825:0.000000 a:@0.469524:0.201354:0.478501:0.201354:0.478501:0.184885:0.469524:0.184885:0.000000 3:@0.478366:0.204515:0.483319:0.204515:0.483319:0.194896:0.478366:0.194896:0.000000 = :@0.483240:0.201238:0.502063:0.201238:0.502063:0.184740:0.483240:0.184740:0.000000:0.000000:0.000000 a:@0.501928:0.201354:0.510905:0.201354:0.510905:0.184885:0.501928:0.184885:0.000000 0:@0.510770:0.204515:0.515723:0.204515:0.515723:0.194896:0.510770:0.194896:0.000000 α:@0.515645:0.208824:0.526222:0.208824:0.526222:0.189825:0.515645:0.189825:0.000000 4:@0.526594:0.194885:0.531547:0.194885:0.531547:0.185267:0.526594:0.185267:0.000000 ,:@0.531469:0.201238:0.534224:0.201238:0.534224:0.184740:0.531469:0.184740:0.000000 a:@0.108231:0.218704:0.117208:0.218704:0.117208:0.202236:0.108231:0.202236:0.000000 n:@0.116922:0.221933:0.122380:0.221933:0.122380:0.212332:0.116922:0.212332:0.000000 +1:@0.122302:0.221865:0.133477:0.221865:0.133477:0.212247:0.122302:0.212247:0.000000:0.000000 = :@0.133399:0.218589:0.152221:0.218589:0.152221:0.202091:0.133399:0.202091:0.000000:0.000000:0.000000 α:@0.152086:0.226175:0.162663:0.226175:0.162663:0.207176:0.152086:0.207176:0.000000 a:@0.163035:0.218704:0.172013:0.218704:0.172013:0.202236:0.163035:0.202236:0.000000 n:@0.171877:0.221865:0.177493:0.221865:0.177493:0.212247:0.171877:0.212247:0.000000 = :@0.177415:0.218589:0.196238:0.218589:0.196238:0.202091:0.177415:0.202091:0.000000:0.000000:0.000000 a:@0.196103:0.218704:0.205080:0.218704:0.205080:0.202236:0.196103:0.202236:0.000000 0:@0.204945:0.221865:0.209898:0.221865:0.209898:0.212247:0.204945:0.212247:0.000000 α:@0.209818:0.226175:0.220395:0.226175:0.220395:0.207176:0.209818:0.207176:0.000000 n:@0.220769:0.212303:0.226228:0.212303:0.226228:0.202702:0.220769:0.202702:0.000000 +1:@0.226149:0.212236:0.237324:0.212236:0.237324:0.202618:0.226149:0.202618:0.000000:0.000000 , = 0, 1, … .:@0.237245:0.218589:0.331452:0.218589:0.331452:0.202091:0.237245:0.202091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.251887:0.218704:0.261249:0.218704:0.261249:0.202236:0.251887:0.202236:0.000000 Sucesiones monótonas:@0.108233:0.254688:0.291065:0.254688:0.291065:0.237005:0.108233:0.237005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición :@0.108233:0.271858:0.195100:0.271858:0.195100:0.254912:0.108233:0.254912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sea ( ) una sucesión real.:@0.188319:0.271395:0.377640:0.271395:0.377640:0.254898:0.188319:0.254898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.229315:0.271511:0.238293:0.271511:0.238293:0.255042:0.229315:0.255042:0.000000 n:@0.238136:0.274740:0.243595:0.274740:0.243595:0.265138:0.238136:0.265138:0.000000 i):@0.108236:0.306314:0.118774:0.306314:0.118774:0.289599:0.108236:0.289599:0.000000:0.000000 Se dice que ( ) es creciente si y solo si ≤ :@0.118775:0.306097:0.442288:0.306097:0.442288:0.289599:0.118775:0.289599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.223057:0.306213:0.232035:0.306213:0.232035:0.289744:0.223057:0.289744:0.000000 n:@0.231884:0.309442:0.237343:0.309442:0.237343:0.299841:0.231884:0.299841:0.000000 a:@0.408915:0.306213:0.417892:0.306213:0.417892:0.289744:0.408915:0.289744:0.000000 n:@0.417739:0.309442:0.423197:0.309442:0.423197:0.299841:0.417739:0.299841:0.000000 a:@0.442288:0.306213:0.451266:0.306213:0.451266:0.289744:0.442288:0.289744:0.000000 n:@0.451113:0.309442:0.456571:0.309442:0.456571:0.299841:0.451113:0.299841:0.000000 +1:@0.456571:0.309375:0.467825:0.309375:0.467825:0.299757:0.456571:0.299757:0.000000:0.000000 , :@0.468386:0.306097:0.479425:0.306097:0.479425:0.289599:0.468386:0.289599:0.000000:0.000000:0.000000 ∀:@0.479424:0.313683:0.490997:0.313683:0.490997:0.294684:0.479424:0.294684:0.000000 n:@0.491005:0.306213:0.500368:0.306213:0.500368:0.289744:0.491005:0.289744:0.000000 .:@0.500368:0.306097:0.531644:0.306097:0.531644:0.289599:0.500368:0.289599:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.504509:0.305578:0.519162:0.305578:0.519162:0.292205:0.504509:0.292205:0.000000 :@0.523304:0.313683:0.528891:0.313683:0.528891:0.294684:0.523304:0.294684:0.000000:0.000000 ii):@0.108232:0.323664:0.123028:0.323664:0.123028:0.306950:0.108232:0.306950:0.000000:0.000000:0.000000 Se dice que ( ) es estrictamente creciente si y solo si < :@0.123029:0.323448:0.510725:0.323448:0.510725:0.306950:0.123029:0.306950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.216041:0.323563:0.225019:0.323563:0.225019:0.307095:0.216041:0.307095:0.000000 n:@0.224332:0.326793:0.229791:0.326793:0.229791:0.317192:0.224332:0.317192:0.000000 a:@0.480713:0.323563:0.489691:0.323563:0.489691:0.307095:0.480713:0.307095:0.000000 n:@0.488993:0.326793:0.494452:0.326793:0.494452:0.317192:0.488993:0.317192:0.000000 a:@0.510147:0.323563:0.519125:0.323563:0.519125:0.307095:0.510147:0.307095:0.000000 n:@0.518392:0.326793:0.523851:0.326793:0.523851:0.317192:0.518392:0.317192:0.000000 +1:@0.523514:0.326726:0.534431:0.326726:0.534431:0.317107:0.523514:0.317107:0.000000:0.000000 , .:@0.534655:0.323448:0.592923:0.323448:0.592923:0.306950:0.534655:0.306950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.543960:0.331034:0.555532:0.331034:0.555532:0.312035:0.543960:0.312035:0.000000 n:@0.554988:0.323563:0.564351:0.323563:0.564351:0.307095:0.554988:0.307095:0.000000 :@0.567336:0.322929:0.581988:0.322929:0.581988:0.309556:0.567336:0.309556:0.000000 :@0.585025:0.331034:0.590612:0.331034:0.590612:0.312035:0.585025:0.312035:0.000000:0.000000 iii):@0.108228:0.341015:0.127281:0.341015:0.127281:0.324301:0.108228:0.324301:0.000000:0.000000:0.000000:0.000000 Se dice que ( ) es decreciente si y solo si :@0.127282:0.340798:0.426928:0.340798:0.426928:0.324301:0.127282:0.324301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.223049:0.340914:0.232027:0.340914:0.232027:0.324445:0.223049:0.324445:0.000000 n:@0.231884:0.344144:0.237343:0.344144:0.237343:0.334543:0.231884:0.334543:0.000000 a:@0.426928:0.340914:0.435905:0.340914:0.435905:0.324445:0.426928:0.324445:0.000000 n:@0.435751:0.344144:0.441209:0.344144:0.441209:0.334543:0.435751:0.334543:0.000000 +1:@0.441209:0.344076:0.452463:0.344076:0.452463:0.334458:0.441209:0.334458:0.000000:0.000000 ≤ , :@0.453024:0.340798:0.497437:0.340798:0.497437:0.324301:0.453024:0.324301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.472116:0.340914:0.481094:0.340914:0.481094:0.324445:0.472116:0.324445:0.000000 n:@0.480940:0.344144:0.486399:0.344144:0.486399:0.334543:0.480940:0.334543:0.000000 ∀:@0.497436:0.348385:0.509009:0.348385:0.509009:0.329386:0.497436:0.329386:0.000000 n:@0.509017:0.340914:0.518380:0.340914:0.518380:0.324445:0.509017:0.324445:0.000000 .:@0.518380:0.340798:0.549658:0.340798:0.549658:0.324301:0.518380:0.324301:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.522522:0.340280:0.537174:0.340280:0.537174:0.326906:0.522522:0.326906:0.000000 :@0.541316:0.348385:0.546903:0.348385:0.546903:0.329386:0.541316:0.329386:0.000000:0.000000 iv):@0.108233:0.358366:0.127036:0.358366:0.127036:0.341651:0.108233:0.341651:0.000000:0.000000:0.000000 Se dice que ( ) es estrictamente decreciente si y solo si :@0.127036:0.358149:0.529243:0.358149:0.529243:0.341651:0.127036:0.341651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.223054:0.358265:0.232032:0.358265:0.232032:0.341796:0.223054:0.341796:0.000000 n:@0.231884:0.361495:0.237343:0.361495:0.237343:0.351893:0.231884:0.351893:0.000000 a:@0.529243:0.358265:0.538221:0.358265:0.538221:0.341796:0.529243:0.341796:0.000000 n:@0.538068:0.361495:0.543526:0.361495:0.543526:0.351893:0.538068:0.351893:0.000000 +1:@0.543526:0.361427:0.554780:0.361427:0.554780:0.351809:0.543526:0.351809:0.000000:0.000000 < , :@0.555341:0.358149:0.596173:0.358149:0.596173:0.341651:0.555341:0.341651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.574433:0.358265:0.583411:0.358265:0.583411:0.341796:0.574433:0.341796:0.000000 n:@0.583257:0.361495:0.588716:0.361495:0.588716:0.351893:0.583257:0.351893:0.000000 ∀:@0.131976:0.383086:0.143549:0.383086:0.143549:0.364087:0.131976:0.364087:0.000000 n:@0.143557:0.375616:0.152920:0.375616:0.152920:0.359147:0.143557:0.359147:0.000000 .:@0.152920:0.375500:0.184198:0.375500:0.184198:0.359002:0.152920:0.359002:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.157061:0.374981:0.171714:0.374981:0.171714:0.361608:0.157061:0.361608:0.000000 :@0.175856:0.383086:0.181443:0.383086:0.181443:0.364087:0.175856:0.364087:0.000000:0.000000 v):@0.108235:0.393067:0.122857:0.393067:0.122857:0.376353:0.108235:0.376353:0.000000:0.000000 Se dice que la sucesión ( ) es monótona si es creciente o decre-:@0.122856:0.392851:0.595747:0.392851:0.595747:0.376353:0.122856:0.376353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.307206:0.392966:0.316184:0.392966:0.316184:0.376498:0.307206:0.376498:0.000000 n:@0.316050:0.396195:0.321508:0.396195:0.321508:0.386594:0.316050:0.386594:0.000000 ciente. :@0.131976:0.410201:0.182143:0.410201:0.182143:0.393704:0.131976:0.393704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108241:0.427552:0.116525:0.427552:0.116525:0.411054:0.108241:0.411054:0.000000:0.000000 Ejercicio resueltos:@0.108241:0.445279:0.232558:0.445279:0.232558:0.428492:0.108241:0.428492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a):@0.108241:0.462471:0.122787:0.462471:0.122787:0.445756:0.108241:0.445756:0.000000:0.000000 La sucesión ( ), cuyo término general está definido como:@0.122788:0.462254:0.544313:0.462254:0.544313:0.445756:0.122788:0.445756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.223369:0.462369:0.232346:0.462369:0.232346:0.445901:0.223369:0.445901:0.000000 n:@0.232192:0.465599:0.237651:0.465599:0.237651:0.455998:0.232192:0.455998:0.000000 :@0.108227:0.486733:0.112369:0.486733:0.112369:0.470236:0.108227:0.470236:0.000000 a:@0.131963:0.486849:0.140940:0.486849:0.140940:0.470380:0.131963:0.470380:0.000000 n:@0.140800:0.490077:0.146258:0.490077:0.146258:0.480476:0.140800:0.480476:0.000000 = , , es una sucesión estrictamente decreciente.:@0.146259:0.486732:0.555585:0.486732:0.555585:0.470234:0.146259:0.470234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.192958:0.486848:0.202321:0.486848:0.202321:0.470379:0.192958:0.470379:0.000000 :@0.206463:0.486515:0.222511:0.486515:0.222511:0.471868:0.206463:0.471868:0.000000 Z:@0.227421:0.485645:0.239713:0.485645:0.239713:0.472783:0.227421:0.472783:0.000000 +:@0.239713:0.477866:0.246013:0.477866:0.246013:0.468248:0.239713:0.468248:0.000000 :@0.108228:0.511212:0.112370:0.511212:0.112370:0.494714:0.108228:0.494714:0.000000 En efecto, si , entonces < + 1 y, en consecuencia, :@0.131963:0.511212:0.564823:0.511212:0.564823:0.494714:0.131963:0.494714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.219329:0.511327:0.228692:0.511327:0.228692:0.494859:0.219329:0.494859:0.000000 :@0.232834:0.510995:0.248882:0.510995:0.248882:0.496348:0.232834:0.496348:0.000000 Z:@0.253808:0.510125:0.266099:0.510125:0.266099:0.497263:0.253808:0.497263:0.000000 +:@0.266099:0.502344:0.272400:0.502344:0.272400:0.492726:0.266099:0.492726:0.000000 n n:@0.348149:0.511327:0.385967:0.511327:0.385967:0.494859:0.348149:0.494859:0.000000:0.000000:0.000000 :@0.108241:0.535690:0.112383:0.535690:0.112383:0.519192:0.108241:0.519192:0.000000 < .:@0.131976:0.535690:0.211811:0.535690:0.211811:0.519192:0.131976:0.519192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108241:0.565115:0.112383:0.565115:0.112383:0.548617:0.108241:0.548617:0.000000 De la definición de ( ) se concluye que :@0.131976:0.565115:0.429740:0.565111:0.429740:0.548613:0.131976:0.548617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.282534:0.565230:0.291512:0.565230:0.291512:0.548762:0.282534:0.548762:0.000000 n:@0.291354:0.568455:0.296812:0.568455:0.296812:0.558854:0.291354:0.558854:0.000000 a:@0.431396:0.565227:0.440374:0.565227:0.440374:0.548758:0.431396:0.548758:0.000000 n:@0.440219:0.568455:0.445677:0.568455:0.445677:0.558854:0.440219:0.558854:0.000000 +1:@0.445677:0.568388:0.456931:0.568388:0.456931:0.558769:0.445677:0.558769:0.000000:0.000000 ≤ ; o sea, ( ) es :@0.457494:0.565111:0.599910:0.565111:0.599910:0.548613:0.457494:0.548613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.479899:0.565227:0.488877:0.565227:0.488877:0.548758:0.479899:0.548758:0.000000 n:@0.488720:0.568455:0.494179:0.568455:0.494179:0.558854:0.488720:0.558854:0.000000 a:@0.555364:0.565227:0.564342:0.565227:0.564342:0.548758:0.555364:0.548758:0.000000 n:@0.564186:0.568455:0.569645:0.568455:0.569645:0.558854:0.564186:0.558854:0.000000 estrictamente decreciente.:@0.131976:0.582462:0.319967:0.582462:0.319967:0.565964:0.131976:0.565964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b):@0.108241:0.617380:0.124251:0.617380:0.124251:0.600665:0.108241:0.600665:0.000000:0.000000 La sucesión 1 – es estrictamente creciente, pues si ,:@0.124252:0.617163:0.582469:0.617163:0.582469:0.600665:0.124252:0.600665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.526660:0.617279:0.536023:0.617279:0.536023:0.600810:0.526660:0.600810:0.000000 :@0.540165:0.616946:0.556213:0.616946:0.556213:0.602299:0.540165:0.602299:0.000000 Z:@0.561122:0.616076:0.573414:0.616076:0.573414:0.603214:0.561122:0.603214:0.000000 +:@0.573414:0.608296:0.579715:0.608296:0.579715:0.598677:0.573414:0.598677:0.000000 entonces < + 1, y se tienen las siguientes equivalencias: :@0.131971:0.641642:0.549889:0.641642:0.549889:0.625144:0.131971:0.625144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n n:@0.200825:0.641757:0.238643:0.641757:0.238643:0.625288:0.200825:0.625288:0.000000:0.000000:0.000000 :@0.108236:0.658992:0.112378:0.658992:0.112378:0.642495:0.108236:0.642495:0.000000 :@0.108236:0.676343:0.112378:0.676343:0.112378:0.659845:0.108236:0.659845:0.000000 < :@0.131971:0.676343:0.213194:0.676343:0.213194:0.659845:0.131971:0.659845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.213194:0.675837:0.233268:0.675837:0.233268:0.658125:0.213194:0.658125:0.000000 – < – :@0.233268:0.676343:0.335489:0.676343:0.335489:0.659845:0.233268:0.659845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.335489:0.675837:0.355564:0.675837:0.355564:0.658125:0.335489:0.658125:0.000000 1 – < 1 – :@0.355564:0.676343:0.495487:0.676343:0.495487:0.659845:0.355564:0.659845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.495487:0.675837:0.515562:0.675837:0.515562:0.658125:0.495487:0.658125:0.000000 < :@0.515562:0.676343:0.551697:0.676343:0.551697:0.659845:0.515562:0.659845:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.519704:0.676459:0.528681:0.676459:0.528681:0.659990:0.519704:0.659990:0.000000 n:@0.528142:0.679688:0.533601:0.679688:0.533601:0.670087:0.528142:0.670087:0.000000 a:@0.551311:0.676459:0.560289:0.676459:0.560289:0.659990:0.551311:0.659990:0.000000 n:@0.559749:0.679688:0.565207:0.679688:0.565207:0.670087:0.559749:0.670087:0.000000 +1:@0.564983:0.679621:0.576012:0.679621:0.576012:0.670003:0.564983:0.670003:0.000000:0.000000 .:@0.576349:0.676343:0.579104:0.676343:0.579104:0.659845:0.576349:0.659845:0.000000 :@0.108242:0.711045:0.112384:0.711045:0.112384:0.694547:0.108242:0.694547:0.000000 Recuerda que si a una desigualdad se la multiplica por –1, la :@0.131976:0.711045:0.599947:0.711045:0.599947:0.694547:0.131976:0.694547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 desigualdad cambia de sentido. Además, si a una desigualdad se :@0.131976:0.728395:0.599900:0.728395:0.599900:0.711898:0.131976:0.711898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 le suma en ambos miembros el mismo número real, la desigual-:@0.131976:0.745746:0.595822:0.745746:0.595822:0.729248:0.131976:0.729248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dad se conserva.:@0.131976:0.763097:0.252419:0.763097:0.252419:0.746599:0.131976:0.746599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c):@0.108241:0.798015:0.122575:0.798015:0.122575:0.781301:0.108241:0.781301:0.000000:0.000000 Considera la sucesión ( ), definida como = + 1 + (–1) , .:@0.122575:0.797798:0.595767:0.797798:0.595767:0.781301:0.122575:0.781301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.288560:0.797914:0.297769:0.797914:0.297769:0.781445:0.288560:0.781445:0.000000 p:@0.297404:0.801144:0.302807:0.801144:0.302807:0.791543:0.297404:0.791543:0.000000 u:@0.419169:0.797914:0.428378:0.797914:0.428378:0.781445:0.419169:0.781445:0.000000 p:@0.428013:0.801144:0.433415:0.801144:0.433415:0.791543:0.428013:0.791543:0.000000 p:@0.450891:0.797914:0.460157:0.797914:0.460157:0.781445:0.450891:0.781445:0.000000 p:@0.533536:0.791514:0.538939:0.791514:0.538939:0.781913:0.533536:0.781913:0.000000 p:@0.548363:0.797914:0.557630:0.797914:0.557630:0.781445:0.548363:0.781445:0.000000 :@0.560903:0.797280:0.575555:0.797280:0.575555:0.783906:0.560903:0.783906:0.000000 N:@0.578860:0.796711:0.593197:0.796711:0.593197:0.783849:0.578860:0.783849:0.000000 :@0.108241:0.815149:0.112383:0.815149:0.112383:0.798651:0.108241:0.798651:0.000000 El recorrido de esta sucesión es el conjunto: :@0.131976:0.815149:0.444089:0.815149:0.444089:0.798651:0.131976:0.798651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 { + 1 + (–1) | } = {2, 1, 4, 3, … , + 1 + (–1) , …}.:@0.151107:0.839628:0.552897:0.839627:0.552897:0.823130:0.151107:0.823130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.161105:0.839744:0.170372:0.839744:0.170372:0.823275:0.161105:0.823275:0.000000 p:@0.247757:0.833343:0.253160:0.833343:0.253160:0.823742:0.247757:0.823742:0.000000 p:@0.266339:0.839743:0.275605:0.839743:0.275605:0.823274:0.266339:0.823274:0.000000 :@0.279362:0.839109:0.294015:0.839109:0.294015:0.825736:0.279362:0.825736:0.000000 N:@0.297788:0.838541:0.312125:0.838541:0.312125:0.825678:0.297788:0.825678:0.000000 p:@0.430403:0.839743:0.439669:0.839743:0.439669:0.823274:0.430403:0.823274:0.000000 p:@0.517054:0.833343:0.522456:0.833343:0.522456:0.823742:0.517054:0.823742:0.000000 :@0.108236:0.864107:0.112378:0.864107:0.112378:0.847609:0.108236:0.847609:0.000000 Esta no es una sucesión creciente ni decreciente; simplemente es :@0.131971:0.864107:0.599880:0.864107:0.599880:0.847609:0.131971:0.847609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una sucesión real.:@0.131971:0.881458:0.255922:0.881458:0.255922:0.864960:0.131971:0.864960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d):@0.108236:0.916376:0.124438:0.916376:0.124438:0.899662:0.108236:0.899662:0.000000:0.000000 La sucesión (– ) es estrictamente decreciente, pues: :@0.124438:0.916159:0.504862:0.916159:0.504862:0.899662:0.124438:0.899662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.233863:0.916275:0.243226:0.916275:0.243226:0.899806:0.233863:0.899806:0.000000 n n:@0.220052:0.933626:0.257870:0.933626:0.257870:0.917157:0.220052:0.917157:0.000000:0.000000:0.000000 < + 1 :@0.229415:0.933510:0.289600:0.933510:0.289600:0.917012:0.229415:0.917012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.289600:0.933004:0.309674:0.933004:0.309674:0.915292:0.289600:0.915292:0.000000 –( + 1) < – :@0.309674:0.933510:0.422954:0.933510:0.422954:0.917012:0.309674:0.917012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.330268:0.933626:0.339631:0.933626:0.339631:0.917157:0.330268:0.917157:0.000000 n, n:@0.402764:0.933626:0.443908:0.933626:0.443908:0.917157:0.402764:0.917157:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.422964:0.941096:0.434536:0.941096:0.434536:0.922097:0.422964:0.922097:0.000000 .:@0.443908:0.933510:0.483935:0.933510:0.483935:0.917012:0.443908:0.917012:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.448049:0.932991:0.462701:0.932991:0.462701:0.919618:0.448049:0.919618:0.000000 N:@0.466843:0.932423:0.481180:0.932423:0.481180:0.919561:0.466843:0.919561:0.000000 1:@0.171745:0.479363:0.180241:0.479363:0.180241:0.462865:0.171745:0.462865:0.000000 n:@0.171321:0.495817:0.180684:0.495817:0.180684:0.479349:0.171321:0.479349:0.000000 1:@0.193945:0.528261:0.202441:0.528261:0.202441:0.511763:0.193945:0.511763:0.000000 n:@0.193521:0.544715:0.202884:0.544715:0.202884:0.528246:0.193521:0.528246:0.000000 1:@0.257934:0.609709:0.266430:0.609709:0.266430:0.593211:0.257934:0.593211:0.000000 n:@0.257510:0.626163:0.266873:0.626163:0.266873:0.609694:0.257510:0.609694:0.000000 1:@0.192915:0.669049:0.201411:0.669049:0.201411:0.652552:0.192915:0.652552:0.000000 n:@0.192491:0.685504:0.201854:0.685504:0.201854:0.669035:0.192491:0.669035:0.000000 1:@0.392077:0.669049:0.400573:0.669049:0.400573:0.652552:0.392077:0.652552:0.000000 n:@0.391653:0.685504:0.401016:0.685504:0.401016:0.669035:0.391653:0.669035:0.000000 1:@0.254649:0.669049:0.263145:0.669049:0.263145:0.652552:0.254649:0.652552:0.000000 n:@0.254225:0.685504:0.263588:0.685504:0.263588:0.669035:0.254225:0.669035:0.000000 1:@0.146127:0.669049:0.154623:0.669049:0.154623:0.652552:0.146127:0.652552:0.000000 n:@0.136051:0.685504:0.145414:0.685504:0.145414:0.669035:0.136051:0.669035:0.000000 +1:@0.145414:0.685388:0.164718:0.685388:0.164718:0.668890:0.145414:0.668890:0.000000:0.000000 1:@0.309575:0.669049:0.318071:0.669049:0.318071:0.652552:0.309575:0.652552:0.000000 n:@0.299499:0.685504:0.308862:0.685504:0.308862:0.669035:0.299499:0.669035:0.000000 +1:@0.308862:0.685388:0.328166:0.685388:0.328166:0.668890:0.308862:0.668890:0.000000:0.000000 1:@0.468828:0.669049:0.477324:0.669049:0.477324:0.652552:0.468828:0.652552:0.000000 n:@0.458753:0.685504:0.468116:0.685504:0.468116:0.669035:0.458753:0.669035:0.000000 +1:@0.468116:0.685388:0.487419:0.685388:0.487419:0.668890:0.468116:0.668890:0.000000:0.000000 1:@0.146246:0.528261:0.154742:0.528261:0.154742:0.511763:0.146246:0.511763:0.000000 n:@0.136170:0.544715:0.145533:0.544715:0.145533:0.528246:0.136170:0.528246:0.000000 +1:@0.145533:0.544599:0.164837:0.544599:0.164837:0.528102:0.145533:0.528102:0.000000:0.000000 a:@0.184262:0.144591:0.193240:0.144591:0.193240:0.128123:0.184262:0.128123:0.000000 0:@0.193240:0.147754:0.198193:0.147754:0.198193:0.138136:0.193240:0.138136:0.000000 dado,:@0.198192:0.144476:0.280252:0.144476:0.280252:0.127978:0.198192:0.127978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.202334:0.144259:0.218382:0.144259:0.218382:0.129612:0.202334:0.129612:0.000000 R:@0.223295:0.143389:0.236600:0.143389:0.236600:0.130527:0.223295:0.130527:0.000000 a:@0.184255:0.161942:0.193232:0.161942:0.193232:0.145473:0.184255:0.145473:0.000000 n:@0.192950:0.165172:0.198409:0.165172:0.198409:0.155571:0.192950:0.155571:0.000000 +1:@0.198330:0.165104:0.209505:0.165104:0.209505:0.155486:0.198330:0.155486:0.000000:0.000000 = :@0.209428:0.161827:0.228250:0.161827:0.228250:0.145329:0.209428:0.145329:0.000000:0.000000:0.000000 α:@0.228113:0.169413:0.238691:0.169413:0.238691:0.150414:0.228113:0.150414:0.000000 a:@0.239064:0.161942:0.248042:0.161942:0.248042:0.145473:0.239064:0.145473:0.000000 n:@0.247906:0.165104:0.253522:0.165104:0.253522:0.155486:0.247906:0.155486:0.000000 , = 0, 1, … ,:@0.253354:0.161827:0.347561:0.161827:0.347561:0.145329:0.253354:0.145329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.267996:0.161942:0.277359:0.161942:0.277359:0.145473:0.267996:0.145473:0.000000 Competencia :@0.685754:0.642393:0.783376:0.642393:0.783376:0.626921:0.685754:0.626921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 socioemocional:@0.685754:0.654961:0.796129:0.654961:0.796129:0.639489:0.685754:0.639489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las decisiones que :@0.685991:0.679436:0.809471:0.679436:0.809471:0.664373:0.685991:0.664373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tomas cada día marcan tu :@0.639448:0.695278:0.811969:0.695278:0.811969:0.680215:0.639448:0.680215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 camino. ¿Estás consciente de :@0.639448:0.711120:0.833357:0.711120:0.833357:0.696057:0.639448:0.696057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que tus acciones influyen en tu :@0.639448:0.726962:0.844456:0.726962:0.844456:0.711899:0.639448:0.711899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 relación con tus compañeros? :@0.639448:0.742804:0.836085:0.742804:0.836085:0.727741:0.639448:0.727741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tú eres el único responsable de :@0.639448:0.758646:0.844792:0.758646:0.844792:0.743583:0.639448:0.743583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tus actos. :@0.639448:0.774488:0.703931:0.774488:0.703931:0.759425:0.639448:0.759425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Analiza:@0.639453:0.906325:0.691784:0.906325:0.691784:0.890852:0.639453:0.890852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 este razonamiento con :@0.691784:0.905902:0.848069:0.905902:0.848069:0.890839:0.691784:0.890839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tus compañeros.:@0.639453:0.921744:0.746643:0.921744:0.746643:0.906681:0.639453:0.906681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Freepik.es:@0.867505:0.879962:0.867505:0.853046:0.856037:0.853046:0.856037:0.879962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ©:@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