$\"\"$

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.

$\"\"$

The series is $\"\"$ .

Consider $\"\"$ .

Apply ratio test:

$\"\"$ .

$\"\"$

Since $\"\"$ , then the series is $\"\"$ is absolutely convergent.

$\"\"$

The series $\"\"$ absolutely converges.