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 $|r|=|\frac{\frac{3}{4}}{\frac{1}{2}}|=1.5\gt1$, thus it does not converge.
