Mathematik-Online problems: Problem 74: Monotone, Bounded and Convergent Sequences

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	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)

[Links]

automatisch erstellt am 13. 12. 2007

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)	$a_n=\sqrt{n+1}-\sqrt{2n-1}$