The series is .

Observe that .

Because the denominators are equal and numerator is 1 greater in .

Consider .

The obtained series is .

Definition of p - series :

The p - series  is convergent if and divergent if .

It is divergent because .

Compare the given series with the series .

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 .

Therefore  is divergent  by part (ii) of the Comparison Test.

 is divergent.