Answer
See below.
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 the sum equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
Here $|r|=|0.5|=0.5\lt1$, thus it converges, with $a_1=4$, thus the sum: $\frac{4}{1-0.5}=8$
