Answer
By Theorem 9.6, the series converges.
Work Step by Step
Th.9.6, Convergence of a Geometric Series:
A geometric series with ratio $r$ diverges when $|r| \geq 1$.
If $0 < |r| < 1$,
then the series converges to the sum $\displaystyle \sum_{n=0}^{\infty}ar^{n}=\frac{a}{1-r},\quad 0 < |r| < 1$.
------------
$\displaystyle \sum_{n=0}^{\infty}\left(\frac{5}{6}\right)^{n}$ is a geometric series with
$r=\displaystyle \frac{5}{6} < 1$
By Theorem 9.6, the series converges.