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Math Help - [SOLVED] Series in terms of integral help

  1. #1
    da`
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    [SOLVED] Series in terms of integral help

    I have attached this which I have having trouble proving.

    Can anyone point me in the right direction on how to start this?
    Last edited by da`; April 11th 2009 at 06:13 AM.
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  2. #2
    da`
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    i can explain the lhs series as
    Last edited by da`; April 11th 2009 at 06:13 AM.
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  3. #3
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    \frac{1}{1+t^b} = \frac{1}{1 - (-t^b)} = 1 - t^b + t^{2b} - t^{3b} + ...

    \frac{t^{a-1}}{1+t^b} = t^{a-1} - t^{a+b-1} + t^{a+2b-1} - t^{a+3b-1} + ...

    \int_0^1 \frac{t^{a-1}}{1+t^b} dt =

    \left[\frac{t^a}{a} - \frac{t^{a+b}}{a+b} + \frac{t^{a+2b}}{a+2b} - \frac{t^{a+3b}}{a+3b} + ... \right]_0^1 = \frac{1}{a} - \frac{1}{a+b} + \frac{1}{a+2b} - \frac{1}{a+3b} + ...
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