# How do I calculate values of series? [duplicate]

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.

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## marked as duplicate by Qiaochu YuanFeb 24 '11 at 16:50

@Bill: In fairness to Qiaochu, I did flag this as a duplicate for moderator attention, so maybe you should be mad at me. (Of course a priori I don't think there is any way to see who flagged what.) Having said that, maybe you are right, but it is definitely a close call . Perhaps the question should be changed to "How do I evaluate $\sum_{n=1}^{\infty}\frac{P(n)}{r^n}$ where $P(n)$ is some polynomial and $0<r<1$." In its current form it really looks like a duplicate, and I don't feel the OP's intent was a discussion on general evaluation of series. (But maybe it was?) –  Eric Naslund Feb 24 '11 at 18:51
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.