Answer
$8$
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.
$|r|=|\frac{1}{2}|=\frac{1}{2}\lt1$, thus it converges.
Hence the sum (since $a_1=4$): $\dfrac{4}{1-(\frac{1}{2})}=\frac{4}{0.5}=8$
