Thread: Help with series summation

Can Any one help me in solving the following summation:

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

?

Originally Posted by Amjad

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?

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

Originally Posted by Amjad

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.

Thanks alot...this was very helpful...