Alternating Series Test :

If the alternating series  satisfies

(i)  ,

(ii) , then the series is convergent.

The series is .

The function  is an increasing function.

The sequence  is eventually increasing.

Thus, the alternating series is not applicable.

Find .

As , then .

Evaluate the limits.

.

Thus the given series is divergent by the Alternating Series Test.

The series is divergent.