Mathematik-Online problems: Problem 75: Limits of Sequences

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	Mathematik-Online problems:
	Problem 75: Limits of Sequences

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#./aufgabe75_en.tex#Find the limits of the sequences:

a) $a_n={\displaystyle{\frac{1}{1+c^n}}}\,, \quad c>0$ b) $a_n={\displaystyle{\left(\frac{n+3}{2n-1}\right)^{\!n}}}$

c) $a_n={\displaystyle{\frac{n^2}{2^n}}}$ d) $a_n={\displaystyle{\sum_{k=0}^n \frac{(-1)^k}{2^{2k}}}}$

e) $a_n={\displaystyle{\frac{n!}{n^n}}}$ f) $a_n={\displaystyle{\left(1-\frac{1}{4}\right)\cdot \left(1-\frac{1}{9}\right)\cdots \left(1-\frac{1}{(n+1)^2}\right)}}$

(Authors: Kimmerle/Roggenkamp/Höllig/Apprich/Höfert)

Solution:

Lösung (german)

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automatisch erstellt am 18. 1. 2017

a)	$a_n={\displaystyle{\frac{1}{1+c^n}}}\,, \quad c>0$	b)	$a_n={\displaystyle{\left(\frac{n+3}{2n-1}\right)^{\!n}}}$
c)	$a_n={\displaystyle{\frac{n^2}{2^n}}}$	d)	$a_n={\displaystyle{\sum_{k=0}^n \frac{(-1)^k}{2^{2k}}}}$
e)	$a_n={\displaystyle{\frac{n!}{n^n}}}$	f)	$a_n={\displaystyle{\left(1-\frac{1}{4}\right)\cdot \left(1-\frac{1}{9}\right)\cdots \left(1-\frac{1}{(n+1)^2}\right)}}$