$\"\"$

The series is $\"\"$ , $\"\"$ .

Consider $\"\"$ .

Hence $\"\"$ .

Substitute the corresponding values in $\"\"$ .

$\"\"$

$\"\"$ \ \

$\"\"$

$\"\"$ .

When the series is converges if $\"\"$ .

$\"\"$

$\"\"$ .

Hence the center of series is $\"\"$ and the radius of convergence is $\"\"$ .

Therefore, the series is converges in the interval $\"\"$ .

$\"\"$

The series is converges in the interval $\"\"$ .