#### Answer

FALSE

#### Work Step by Step

Let $c_{n}=\frac{(-1)^{n}}{n6^{n}}$
Then
$c_{n}6^{n}=\frac{(-1)^{n}}{n}$, which converges by the Alternating Series Test.
and
$ \sum c_{n}(-6)^{n}$ is diverges, because it is a p-series.
Hence, the statement is false.