The integral Test :

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

The integral series is .

Let the function be .

Find the derivative of the function.

 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 using integration by parts.

Formula for integration by parts is .

Here  and .

Consider .

Apply derivative on each side with respect to .

.

Consider .

Apply integral on each side.

.

Substitutecorresponding values in .

.

Therefore, the series  is converges.

The series  is converges.