Answer
Convergent
Work Step by Step
The Comparison Test:
$|cosx|\leq 1$ for all $x$
The geometric series $\Sigma_{n=1}^\infty r^{n}$ is convergent if $|r|\lt 1$ and divergent if $|r|\geq 1$
$|a_{n}|=\frac{|cos3n|}{1+(1.2)^{n}}\leq \frac{1}{1+(1.2)^{n}} \lt \frac{1}{(1.2)^{n}}=\frac{1}{(1.2)^{n}}$
Since, $\Sigma_{n=1}^\infty\frac{1}{(1.2)^{n}}$ is convergent.
Hence, $\Sigma_{n=1}^\infty|a_{n}|$ is convergent.
