Alternating Series Test: \ \

If the alternating series  satisfies

(i)  ,

(ii) , then the series is convergent.

The series is .

.

The function  is increasing because numerator is increasing

Therefore, the sequence  is eventually increasing.

Thus,the alternating series is not applicable.

Find .

As , then .

Evaluate the limits.

.

Thus, the series is oscillates in between and .

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

The series is divergent.