Answer
$\dfrac{1000}{9}$
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 $r=\dfrac{10}{100}=\dfrac{1}{10}$ and $a_1=100$
We see that $|r|=\left|\dfrac{1}{10}\right| \lt 1$, so the series converges and the sum can be found using the formula above::
$$S_\infty=\dfrac{100}{1-\frac{1}{10}}=\dfrac{1000}{9}$$
