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. \ \

and monotonically increasing. \ \

Therefore, .

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 convergent because .

Therefore, the series is convergent.

is convergent.