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Math Help - find convergent set of the power series

  1. #1
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    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.
    =========================================

    thanks for any help.
    Last edited by rcmango; January 31st 2007 at 08:37 AM. Reason: there are two problems. also, i put it in the urgent section for the second problem.
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  2. #2
    Grand Panjandrum
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    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
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  3. #3
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    ..also, in the first example, why did we take a sqrt of the absolute value equation?
    Last edited by rcmango; January 31st 2007 at 08:36 AM.
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