The series is .

Alternating Series Test :

If the alternating series  satisfies

(i)  ,

(ii) ,

Then the series is convergent.

Verify condition (i) :

Since the series is alternating, verify condition (i) and (ii) of the Alternating Series Test.

It is not obvious that the sequence given by  is decreasing.

So consider the related function .

Apply derivative on each side with respect to .

.

, for all positive numvbers.

The series does not satisfies condition of alternating series test.

Thus, the given series is divergent.

The series  is divergent.