Suppose $A$, $B$ and $C$ are positive constants with $A,B,C \in (0,1)$. I have the following summation:
$1+A(1-BC)+A^2(1-BC)(1-B^2C)+A^3(1-BC)(1-B^2C)(1-B^3C)+...$
$\Rightarrow \sum_{i=0}^{\infty}A^i\Pi_{s=0}^{i-1}(1-B^{s}C)$
(probably the product can be better defined since is not well defined at $i=0$).
The question is: does exist a way to analytically solve for the summation as a function of the parameters? I'm wondering if there is something in the spirit of $\sum_{i=0}^{\infty}A^i = \frac{1}{1-A}$ since the product is between bounded parameters.
Thanks a lot.