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Mathematik-Online problems:

Problem 74: Monotone, Bounded and Convergent Sequences


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

Analyse if the following sequences are monotone, bounded or convergent. Find the limit of each convergent sequence.

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

(Authors: Kimmerle/Roggenkamp/Apprich/Höfert)

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  automatisch erstellt am 13. 12. 2007