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 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.