The integral Test :

If is positive, continuous 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.

Integral Test:

Consider .

.

Consider integral .

Solve the integral by integration by parts.

Integration by parts formula: .

Substitute and .

Consider .

Apply derivative on each side with respect to .

.

Consider .

Apply integral on each side.

.

Substitute corresponding values in .

.

.

Therefore, the series is converges.

The series is converges.