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UBA - CienciaS • Ver Tema - Intercambio entre sumatoria y límite
UBACS Q&A Foro WikiCS
Fecha actual 27 Jun 2022, 02:38

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 Asunto: Intercambio entre sumatoria y límite
NotaPublicado: 08 Sep 2013, 22:11 
Vago

Registrado: 08 Sep 2013, 22:04
Mensajes: 4
Hola a todos:

Necesito ayuda para el siguiente problema.

Sean funciones tales que para cada n, el existe y es igual a .

Si la serie (con la norma supremo) es convergente entonces la serie converge y





Muchas gracias y saludos. :)


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 Asunto: Re: Intercambio entre sumatoria y límite
NotaPublicado: 09 Sep 2013, 17:18 
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Registrado: 05 Jul 2008, 14:02
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Si escribís lo que intentaste y donde te trabaste te doy una mano...



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Quimey
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 Asunto: Re: Intercambio entre sumatoria y límite
NotaPublicado: 10 Sep 2013, 11:16 
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Registrado: 08 Sep 2013, 22:04
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Hola Quimey: (¿El mismo del Rincón Matemático?)
Gracias por contestar.
De todos modos ya pude resolver el problema.
En este orden:

1) Demostré que converge en norma y por lo tanto uniformemente.

2) Demuestro que converge.

3) Con los resultados anteriores, uso la definición de límite para demostrar que
.

¿Me podrás dar un contraejemplo de que no se puede hacer el intercambio entre suma y límite cuando no es convergente?

Gracias y saludos. :)


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 Asunto: Re: Intercambio entre sumatoria y límite
NotaPublicado: 10 Sep 2013, 16:41 
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No soy el mismo de rincon matemático. Después veo si puedo encontrar el contraejemplo.



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Quimey
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 Asunto: Re: Intercambio entre sumatoria y límite
NotaPublicado: 12 Sep 2013, 09:01 
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