Alternating Series Test :

If the alternating series  satisfies

(i) ,

(ii) , then the series is convergent.

The series is .

Rewrite the series as .

The function  is decreasing because the denominator is increasing.

Therefore, the sequence  is eventually decreasing.

Thus, condition (i) is verified.

Find .

As , then .

Evaluate the limits.

.

.

Thus, condition (ii) is verified.

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

The series is convergent.