$\"\"$

Integral test:

Suppose $\"\"$ is a continuous, positive, decreasing function on $\"\"$ and let $\"\"$ .

Then the series $\"\"$ is convergent if and only if the improper integral $\"\"$ is convergent.

(i) If $\"\"$ is convergent, then $\"\"$ is convergent.

(ii) If $\"\"$ is divergent, then $\"\"$ is divergent.

$\"\"$

The series is $\"\"$ .

Apply integral test.

Consider the integral $\"\"$ .

$\"\"$

$\"\"$ .

The integral is diverges.

Therefore, the series $\"\"$ is diverges.

$\"\"$

The series $\"\"$ is diverges.