Answer
$4$
Work Step by Step
The sum of an infinite geometric series exists only if $|r|\lt 1$ and, thus the series converges.
The sum of an infinite geometric series is given by:
$S_\infty=\dfrac{a_1}{1-r}$
From the given geometric series we have $r=\dfrac{1}{4}$ and $a_1=(3)\left(\dfrac{1}{4}\right)^{1-1}=3$
We see that $|r|=\left|\dfrac{1}{4}\right| \lt 1$, so the series converges and their sum can be found using the formula above:
$$S_\infty=\dfrac{3}{1-\frac{1}{4}}=\dfrac{4}{3}\times 3=4$$
Therefore, the sum of an infinite geometric series is: $S_{\infty}=4$
