Answer
$20$
Work Step by Step
An infinite geometric series converges if and only if $|r|\lt1$, where $r$ is the common ratio. If it converges, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
Here $|r|=0.9\lt1$, thus it converges, with $a_1=1,r=0.95$, thus the multiplier: $\frac{1}{1-0.95}=20$
