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.