The series is .

Ratio Test :

(i) If , then the series is  is absolutely convergent.

(ii) If  or , then the series is  is divergent.

(iii) If , then the ratio test is inconclusive.

Apply ratio test.

Since , then the ratio test is inconclusive.

So apply any alternate method to test the convergence of the series. 

Test for convergence for the series using alternating series test.

Alternating series test :

Suppose we have the series such that or

where for all values of .

Then if the following two conditions are satisfied the series is convergent.

(1) is a decreasing sequence.

(2) .

Condition 1 :

Because if then .

If for since .

Hence is decreasing for .

Condition 2 :

.

Divide both numerator and denominator by .

Hence the series is convergent by alternate series test.

The series is conditionally convergent.