Answer
$S_{\infty}=\dfrac{81}{5}$
Work Step by Step
Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $
18,-2,\dfrac{2}{9},...
$ is
\begin{array}{l}
S_{\infty}=\dfrac{18}{1-\left(-\dfrac{1}{9}\right)}\\\\
S_{\infty}=\dfrac{18}{\dfrac{10}{9}}\\\\
S_{\infty}=\dfrac{81}{5}
.\end{array}