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How can I evaluate $\sum_{n=1}^\infty \frac{2n}{3^{n+1}}$

I need to compute the sum of $$\sum_{n=1}^{\infty}\frac{n}{2^n}$$ using power series.

Any hints of how should I do that?

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    @Jozef: Note that in the answers to the question linked by Didier you have $\sum nr^{n}$. Your question is a special case for $r=1/2$. (Other questions linked to that one might have answers interesting for you too.)2011-12-26

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