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Math Help - Alternating series

  1. #1
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    Alternating series

    I need to prove
    \sum_{n=1}^{\infty} (-\lambda)^n\prod_{i=1}^n \left(1 + \frac{a}{b+i}\right) < \sum_{n=1}^{\infty} (-\lambda)^n\left(1 + \frac{a}{b+1}\right)^n
    where \lambda, a and b are positive constants such that
    \left|\lambda\left(1 + \frac{a}{b+1}\right)\right| < 1.

    Of course,
     \sum_{n=1}^{\infty} (-\lambda)^n\left(1 + \frac{a}{b+1}\right)^n = \frac{(-\lambda)\left(1 + \frac{a}{b+1}\right)}{1+\lambda\left(1 + \frac{a}{b+1}\right)}
    but this doesn't help me.

    Thanks in advance!
    Last edited by sander; August 1st 2012 at 07:51 AM.
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