Alternating Series Test :

If the alternating series  satisfies

(i)  ,

(ii) , then the series is convergent.

The series is .

The function ,  is decreasing and cosine function is an decreasing function.

Therefore, the sequence  is eventually decreasing .

Thus, condition (i) is verified.

Find .

As , then .

.

Thus, condition (ii) is not verified.

Therefore,  the given series is divergent by the Alternating Series Test.

The series is divergent.