The integral Test:

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

The integral series is .

The summation notation of series is .

Let the function be .

Find the derivative of the function.

.

for .

is positive, continuous and decreasing for .

satisfies the conditions of Integral Test.

Integral Test is applicable for the series.

.

Integrate on each side.

.

Apply integrate by parts: .

Let .

Apply drivative on each side.

Integrate on both side.

Substitute , ,  and .

Apply LHopitals Rule :

For If or then .

The series converges.

The series converges.