$\"\"$

The series is $\"\"$ .

Alternative series test:

If the series is $\"\"$ , then test for convergence is $\"\"$ and $\"\"$ .

Here $\"\"$ and $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ .

Therefoe, the series $\"\"$ is converges by using alternating series test. $\"\"$

The series $\"\"$ is converges by using alternating series test.