# Math Help - Help with series summation

1. ## Help with series summation

Can Any one help me in solving the following summation:

Sum (1 to Inf) [ n / (2^n)]

?

Can Any one help me in solving the following summation:

Sum (1 to Inf) [ n / (2^n)]

?
Do you need a proof? Or is this ok? $x\left(\frac{1}{1-x}\right)'=\sum_{n=0}^{\infty}nx^n\quad\forall{x}\ backepsilon|x|<1$

3. ## Thanks

Thank you very much ... can you post a brief proof?

Just consider that for every interior point of a series interval of convergence it is uniformly convergent. So the derivative of the series is the derivative of the inside of the series i.e. $\frac{d}{dx}\sum_{f_n(x)}=\sum\frac{d}{dx}f_n(x)$