The series is .

Alternating Series Test :

If the alternating series  satisfies

(i)  ,

(ii) ,

Then the series is convergent.

Consider .

Verify condition (i) :

It is obvious that the sequence given by is decreasing.

Verify condition (ii) :

The series satisfies conditions of alternating series test.

Thus, the given series is convergent by Alternating series test.

The series is convergent.