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Math Help - Help with Summations

  1. #1
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    Help with Summations

    Hey,

    I am having trouble with the following proof.

    If Pj = ∑ Qj (limits i = j+1 to ∞), then how do you prove that : ∑ Pj (limits 0 to ∞) = ∑ j*Qj (limits j+1 to ∞)

    Cheers.
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: Help with Summations

    If
    P_j = \sum\limits_{i=j+1}^\infty Q_i, then
    \sum\limits_{j=0}^\infty P_j = \sum\limits_{j=0}^\infty (\sum\limits_{i=j+1}^\infty Q_i)= (\sum\limits_{i=1}^\infty Q_i) + (\sum\limits_{i=2}^\infty Q_i) + ... + (\sum\limits_{i=j+1}^\infty Q_i)

    If you can show (\sum\limits_{i=1}^\infty Q_i) = (\sum\limits_{i=2}^\infty Q_i) = ... = (\sum\limits_{i=j+1}^\infty Q_i) then you are done (since there are j terms in the sum). Otherwise I'm stumped.
    Last edited by MacstersUndead; March 2nd 2013 at 10:39 PM.
    Thanks from banker
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  3. #3
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    Re: Help with Summations

    Cheers man, managed to do it. Same logic but a different intermediary step!
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  4. #4
    Senior Member MacstersUndead's Avatar
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    Re: Help with Summations

    I'm curious to what the different intermediary step is.
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