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Math Help - Find the radius of convergence of a given power series.

  1. #1
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    Find the radius of convergence of a given power series.

    given \sum\frac{(x-2)^n}{n^n} find the radius of convergence.

    so i first substitute y in for x.

    and then i use the ratio test.

    giving me;

    |y|*\lim_{n\rightarrow\infty} \frac{n^n}{(n+1)^{(n+1)}}

    i don't see any simplifications.

    i tried l'Hospitals rule and ended up taking an infinite amount of derivatives to get;

    |y|*\lim_{n\to\infty}\frac{n^n}{(n+1)!}

    which doesn't seem helpful. (even if i didn't flub something along the way which seems unlikely.)
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  2. #2
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    Re: Find the radius of convergence of a given power series.

    You should use the root test.

    - Hollywood
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