Mathematik-Online problems: Problem 94: Definition and Determination of Limit

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	Mathematik-Online problems:
	Problem 94: Definition and Determination of Limit

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 the sequence

with

$\displaystyle a_n = \frac{1}{\sqrt{2n}-\sqrt{n}}\,.$

a): Find ${\displaystyle{a:=\lim_{n\to\infty} a_n}}$ .
b): Find for each constant $\varepsilon=1$ , $\varepsilon=10^{-3}$ and $\varepsilon=10^{-6}$ the smallest index $n_0\in\mathbb{N}$ , so that $\vert a_n - a\vert < \varepsilon$ , for all .

(Authors: Werner/Walk/Höfert)

Solution:

automatisch erstellt am 14. 10. 2004