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Math Help - Help with series summation

  1. #1
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    Help with series summation

    Can Any one help me in solving the following summation:

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

    ?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Amjad View Post
    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
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  3. #3
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    Thanks

    Thank you very much ... can you post a brief proof?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Amjad View Post
    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)
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  5. #5
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    Thanks alot...this was very helpful...
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