[SOLVED] Series in terms of integral help

**da`** · April 11th 2009, 05:47 AM

I have attached this which I have having trouble proving.

Can anyone point me in the right direction on how to start this?

**da`** · April 11th 2009, 05:55 AM

i can explain the lhs series as

**skeeter** · April 11th 2009, 06:00 AM

$\frac{1}{1+t^b} = \frac{1}{1 - (-t^b)} = 1 - t^b + t^{2b} - t^{3b} + ...$

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

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

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

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