Mathematik-Online problems: Problem 76: Accumulation Points and Convergent Subsequences

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	Mathematik-Online problems:
	Problem 76: Accumulation Points and Convergent Subsequences

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

Find all accumulation points of the following sequences. Give for each accumulation point a subsequence

that converges against this point.

a) $a_n={\displaystyle{\sin\,\frac{n\pi}{6}}}$ b) $a_n={\displaystyle{\frac{(-1)^n}{n}}}$

c) $a_n={\displaystyle{\frac{(-1)^n(1-n)}{2n+1}}}$ d) $a_n=(-1)^{\frac{1}{2}n(n+1)}$

e) $a_n=n\,(-1)^n$ f) $a_n=\min\,\{n, 1000\}$

(Authors: Kimmerle/Roggenkamp/Apprich/Höfert)

see also:

Keyword: Sequence
Keyword: Accumulation point

automatisch erstellt am 12. 12. 2007

a)	$a_n={\displaystyle{\sin\,\frac{n\pi}{6}}}$	b)	$a_n={\displaystyle{\frac{(-1)^n}{n}}}$
c)	$a_n={\displaystyle{\frac{(-1)^n(1-n)}{2n+1}}}$	d)	$a_n=(-1)^{\frac{1}{2}n(n+1)}$
e)	$a_n=n\,(-1)^n$	f)	$a_n=\min\,\{n, 1000\}$