## upper bound for series

Hello all,

I would like to find an upper bound for

$\sum_{i=0}^{\infty} \left(a + \frac{1}{b + ci}\right)^i$

where

$0 < a < 1, b > 0, a + \frac{1}{b} < 1, c> 0$

Of course,

$\sum_{i=0}^{\infty} \left(a + \frac{1}{b + ci}\right)^i \leq \sum_{i=0}^{\infty} \left(a + \frac{1}{b}\right)^i = \frac{1}{1 - (a + \frac{1}{b})}$

is an upper bound. Is a more strict upper bound available which includes $c$?