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  .

.

Substitute in .

If then .

  for .

The limit approaches infinity for all real numbers except at , therefore .

Therefore, the series is converges in the interval .

The radius of the convergence is .

The radius of the convergence is and the series is converges in the interval .