The series is .

Here .

.

Let us consider .

Compare the given series with the series .

It is geometric series with common ratio .

Geometric series with , is convergent.

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 .

Series less than the converging series is also convergent.

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

is convergent.