The series is .

Ratio test :

Let be a series with non zero terms.

1. converges absolutely if .

2. diverges if or .

3. The ratio test is inconclusive if .

Consider .

Find .

.

\

LHospitals Rule :

 If the value of limit is indeterminate form of type  or , then

.

\

Therefore by the ratio test series is convergent.

is convergent.