# Finding function represented by power series

• April 12th 2009, 07:58 AM
andreas
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.
• April 12th 2009, 08:48 AM
Nacho
I think that $
\left| z \right| < 1
$

this is my help: $
f(z) = \sum\limits_{k = 0}^\infty {z^k } = \frac{1}
{{1 - z}} \Rightarrow f'(x) = \sum\limits_{k = 0}^\infty {kz^{k - 1} }
$
• April 12th 2009, 09:37 AM
andreas
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.