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 , the ratio test is inconclusive.

Now check the convergence of .

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) for all values of .

(2).

.

Condition 1: 

Substiute for different values of :

The values are decreasing, therefore for all values of .

Therefore the condition 1 is satisfied.

Condition 2 : 

Hence the series is convergent by alternate series test.

The series is conditionally convergent.