The series is .

Here .

Check whether the function is decreasing or not.

Differentiate on each side.

Test the function for .

As the function is decreasing.

Thus, the function is continuous and decreasing.

Perform integral test.

Integral test:

If is convergent then is convergent.

Here .

Find .

.

Formula for integration by parts :.

Let and

.

Apply integral on each side.

Substitute corresponding values in the integration by parts formula.

Consider .

.

Again apply integration by parts.

Let and .

.

Substitute corresponding values in the integration formula.

Substitute above result in (1).

Apply L hospital rule for .

= a finite number.

Therefore,  is convergent.

Thus by the integral test series is also convergent.

Series is convergent.