The series is .

Consider the series .

.

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.

Here .

Thus, by the comparision test series less than the converging series is also convergent.

Therefore is convergent  by part (i) of the Comparison Test.

is convergent.