The integral Test :

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

The 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 . \ \

Substitute .

Apply derivative on each side with respect to .

.

Substitute and  in .

Substitute .

.

.

Therefore, the series is diverges.

The series   is diverges.