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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- Apr 12th 2009, 07:58 AMandreasFinding 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. - Apr 12th 2009, 08:48 AMNacho
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} }

$ - Apr 12th 2009, 09:37 AMandreas
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.