How do I calculate values of series? Possible Duplicate:
  How to find the sum of the following series  




Hey there,

How do I (generally) calculate values of series? What tricks and theorems are there to make my life easier? E.g.:
$$\sum_{n=1}^\infty \frac{n^2}{2^n} = ?$$

I know perfectly well how to show whether a series converges or diverges, but (at least in this and a lot of other cases) I have no idea how to calculate the value to which it converges. I'm looking forward to your help.
Consider the more general problem $\sum {n^2}{z^n}$. To handle this, start with $\sum {z^n}$ and $\sum {n}{z^n}$. The first of these should be easy.
Consider the more general problem $\sum {n^2}{z^n}$. To handle this, start with $\sum {z^n}$ and $\sum {n}{z^n}$. The first of these should be easy.