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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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    @Quaochu: In fact, I only accepted the answer because I always accept answers, which helped me. If later on I see an answer more fitting what I was asking for, I accept that answer instead. I don't feel like I did something wrong but tell me if I did. I am of the same opinion that this indeed is not a duplicate but a much more general question.2011-02-24

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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.