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Thread: 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 $\displaystyle \sum k^3z^k$
    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 $\displaystyle
    \left| z \right| < 1
    $

    this is my help: $\displaystyle
    f(z) = \sum\limits_{k = 0}^\infty {z^k } = \frac{1}
    {{1 - z}} \Rightarrow f'(x) = \sum\limits_{k = 0}^\infty {kz^{k - 1} }
    $
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  3. #3
    Junior Member
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    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 $\displaystyle 1/(1-z)$ and of it's sum representations.
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