Alternating Series Test :

If the alternating series  satisfies

(i)  

(ii) 

Then the series is convergent.

The series is .

Verify condition (i) :

So consider the related function .

Differentiate the function with respect to x .

Since we are considering only positive x , consider .

The above statement is false.

Since the above statement is false, the series does not satisfies condition (i) of alternating series test.

Thus, the given series is divergent.

The series  is divergent.