The integral Test :

If is positive, continous, and decreasing for and then and either converge or both diverge.

The series is .

The summation notation of series is .

Let the function be .

The function is continuous and positive for all values of .

Apply integration by parts formula :.

Here then .

Here then .

Apply LHopitals Rule to bring the limit to the determinant form.

For If or then .

The series is converges.

The series is converges by the integral test.