$\"\"$

The series is $\"\"$ .

Limit comparision test :

The series is $\"\"$ .

If $\"\"$ and $\"\"$ divergence, then the series divergence.

If $\"\"$ and $\"\"$ convergence, then the series convergence.

Consider $\"\"$ and $\"\"$ .

$\"\"$

$\"\"$ and $\"\"$ is convergence.

Therefore, the series $\"\"$ is converges by using limit comparison test with $\"\"$ for geometric series.

$\"\"$

The series $\"\"$ is converges.