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Math Help - Using Power Series to find this sum

  1. #1
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    Using Power Series to find this sum

    Can anyone help me on this? I'm trying to find the sum of

    \sum_1^\infty \frac{k}{3^{2k}} using power series.

    This looks like a geometric sequence to me, but I can't get it in a form that lets me use a power series... any help?
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  2. #2
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    \sum\limits_{k = 1}^\infty  {x^k }  = \frac{x}{{1 - x}}
    Differenate to get \sum\limits_{k = 1}^\infty  {kx^{k-1} }  = \frac{1}{{(1 - x)^2}}
    Multiply by x \sum\limits_{k = 1}^\infty  {kx^{k} }  = \frac{x}{{(1 - x)^2}}.
    In your problem let x=\frac{1}{9}.
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