Say I have a fraction and I want to recursively multiply it by itself like so:
$$\sum_{x=1}^{\infty} \left(\frac ab\right)^x$$
where $\frac ab \leq 1$.
Is there a way in which I can simplify this so that it can be run in a computer program? I know that $(a/b)^x$ will approach zero so maybe there is some nice solution.
