$\"\"$

\

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 the given series with the series $\"\"$ .

\

Observe that $\"\"$ .

\

$\"\"$

\

The obtained series is $\"\"$ .

\

$\"\"$

\

Definition of p - series :

\

The p - series $\"\"$ is convergent if $\"\"$ and divergent if $\"\"$ .

\

From the series $\"\"$ .

\

It is divergent because $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$ is divergent.