# Math Help - Alternating series

1. ## 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!