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.

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

Limit comparision Test :

Suppose we have two series and such that for all values of ,

then if then either both series converges or both deries diverges.

Use limit comparision test with and .

The series converges absolutely because is converging.

The series is converges.