find convergent set of the power series

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January 30th 2007, 09:18 PM
rcmango

find convergent set of the power series

'find the convergence set of the given power series for the problem'

heres the equation for problem1: http://img297.imageshack.us/img297/9654/untitledsz2.jpg

The hint for the first one is: to use the root test, so how is this done.
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thanks for any help.
January 31st 2007, 02:44 AM
CaptainBlack

Determine when:

$\sum_{n=1}^{\infty} n^n x^n$

By the root test this would converge absolutly if $C<1$ and diverge if $C>1$ where:

$C=\lim\ \rm{sup}_{n \to \infty} \root n \of {|n^n x^n |}$

and in this case as ${|n^n x^n |} \to \infty$ as $n$ becomes large for all $x \ne 0$ this series diverges.

RonL
January 31st 2007, 05:47 AM
rcmango

..also, in the first example, why did we take a sqrt of the absolute value equation?

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