$\"\"$

The series is $\"\"$ .

Ratio test :

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

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

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

Here $\"\"$ and $\"\"$ .

Find $\"\"$ .

$\"\"$

By the ratio test, the series $\"\"$ is convergent when $\"\"$ .

Radius of convergence is $\"\"$ .

$\"\"$

Interval of convergence is $\"\"$ .

$\"\"$

Radius of convergence is $\"\"$ .

Interval of convergence is $\"\"$ .