Answer
$32$
Work Step by Step
An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. If it exists, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here $r=\frac{3}{4}=0.75,a_1=8(0.75)^{1-1}=8$ $r=|0.75|\lt1$, thus the sum exists.
Hence the sum: $\dfrac{8}{1-0.75}=32$
