The series is .

.

Consider .

The series is a -series with .

-series test:

The -series is convergent if and divergent .

Thus the series is convergent.

Compare the series with .

.

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.

Thus, series less than the converging series is also convergent.

  is convergent  by part (ii) of the comparison Test.

Therefore, is also convergent.

is also convergent.