## College Algebra (10th Edition)

$\frac{4}{3}$
An infinite geometric series converges if and only if $|r|\lt1$, where $r$ is the common ratio. If it converges, then the sum equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here $|r|=|-1/2|=0.5\lt1$, thus it converges, with $a_1=2$, thus the multiplier: $\frac{2}{1-(-0.5)}=\frac{4}{3}$