thanks alot, both answers help alot,

just to make sure i've got it can you just double check I'm doing this right?

$\displaystyle

S = \sum\limits_{n = 0}^\infty {n^2 } x^n

$

factor out the x

$\displaystyle

s = x\sum\limits_{n = 0}^\infty {nx^{n - 2} }

$

(derivative of

$\displaystyle

\sum\limits_{n = 0}^\infty {nx^{n - 1} }

$)

so..

$\displaystyle

\begin{gathered}

s = x.\left( {\frac{1}

{{1 - x}}} \right)'' \hfill \\

= x.\left( {\frac{1}

{{1 - x^3 }}} \right) \hfill \\

\sum\limits_{n = 0}^\infty {n^2 \left( {\frac{9}

{{10}}} \right)^n = \frac{9}

{{10}}.\frac{1}

{{(1 - \frac{9}

{{10}})^3 }} = 900} \hfill \\

\end{gathered}

$

Close??