Ratio test :

The ratio test for absolute convergence of is :

Let

1.If , then the series converges absolutely.

2. If , then the series diverges.

3.If , then additional investigation required.

The series is .

Consider .

The value of  .

.

Find .

.

The series is converges when .

.

Therefore, the series is converges in the interval .

The radius of the convergence is .

The radius of the convergence is .

The series convergence on the interval .