$\"\"$

The series is $\"\"$ .

Find the convergence of the series by Ratio test.

$\"\"$

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.

Find $\"\"$ .

$\"\"$

Where $\"\"$ is a sequence of positive terms and converges to $\"\"$ .

Limit formula: $\"\"$ .

$\"\"$

$\"\"$ $\"\"$ , hence the series $\"\"$ is absolutely convergent.

$\"\"$

The series $\"\"$ is absolutely convergent.