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.

As , .

Since , then the ratio test is inconclusive.

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

Now check the convergence of using alternate 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 : 

.

The value of decreases as the denominator increases.

Condition 2 :

.

Hence the series is convergent by alternate series test.

The series is conditionally convergent.