Step 1:

The series is $\"\"$ .

Rewrite the series as $\"\"$ .

The summation notation of series is $\"\"$ .

Let the function be $\"\"$ .

The function is continuous and positive for all values of $\"\"$ .

Find the derivative of the function.

$\"\"$

Apply quotient rule in derivatives $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$ the function is decreasing for $\"\"$ .

$\"\"$ is positive, continuous and decreasing for $\"\"$ .

$\"\"$ is satisfies the conditions of Integral Test.

Integral Test is applicable for the series series.

Step 2:

$\"\"$

Apply formula $\"\"$ .

In this case $\"\"$ .

$\"\"$

The series is converges.

Solution:

The series is converges.