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Mathematik-Online problems:

Problem 126: Convergence of Sequences and Series

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Given a sequence $ (a_n)$ with

$\displaystyle \frac{1}{n}\leq \vert a_n\vert \leq \frac{4}{\sqrt{n}}\,, \ \ {\mbox{for all}} \ n\in\mathbb{N}. $


a)
Show that $ (a_n)$ has a limit, and find this limit.
b)
What can be said about the convergence of the series $ {\displaystyle{\sum_{n=1}^\infty\, a_n}}$ and $ {\displaystyle{\sum_{n=1}^\infty\, \vert a_n\vert}}$ ?

(Authors: /Höfert)

Solution:

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  automatisch erstellt am 12.  4. 2005