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Math Help - Finding function represented by power series

  1. #1
    Junior Member
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    Finding function represented by power series

    I have to find function represented by \sum k^3z^k
    from k=1 to infinity.

    I tried Taylor's expansion but it did not help me.
    I am trying to solve this for couple of hours. Please give me a hint, or some suggestion.

    thank you.
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  2. #2
    Member Nacho's Avatar
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    Santiago, Chile
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    I think that <br />
\left| z \right| < 1<br />

    this is my help: <br />
f(z) = \sum\limits_{k = 0}^\infty  {z^k }  = \frac{1}<br />
{{1 - z}} \Rightarrow f'(x) = \sum\limits_{k = 0}^\infty  {kz^{k - 1} } <br />
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  3. #3
    Junior Member
    Joined
    Nov 2008
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    I finally managed to solve the problem, thanks to your suggestion.

    The idea is to consider three derivatives of 1/(1-z) and of it's sum representations.
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