$\"\"$

The series is $\"\"$ .

The Comparison Test :

Suppose that $\"\"$ and $\"\"$ are series with positive terms.

(i) If $\"\"$ is convergent and $\"\"$ for all n , then $\"\"$ is also convergent.

(ii) If $\"\"$ is divergent and $\"\"$ for all n, then $\"\"$ is also divergent.

The dominant part of the numerator is $\"\"$ and the dominant part of the denominator is $\"\"$ .

The series is $\"\"$ .

Compare $\"\"$ with the series $\"\"$ .

Observe that $\"\"$ .

$\"\"$

The obtained series is $\"\"$ .

$\"\"$ .

The series $\"\"$ is a geometric series with $\"\"$ .

If $\"\"$ , then the series is diverges.

Therefore, the series $\"\"$ is divergent.

$\"\"$

$\"\"$ is divergent.