Answer
$27$
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 the formula:
$$S_\infty=\dfrac{a_1}{1-r}$$
From the given geometric series we have $r=\dfrac{6}{18}=\dfrac{1}{3}$ and $a_1=18$
We see that $|r|=\left|\dfrac{1}{3}\right| \lt 1$, so the series converges and their sum can be found using the formula above:
$$S_\infty=\dfrac{18}{1-\frac{1}{3}}=\dfrac{18}{\frac{2}{3}}=27$$