$\"\"$

The function is $\"\"$ .

$\"\"$

The power series is $\"\"$ .

$\"\"$

According to the ratio test $\"\"$ .

For the series $\"\"$ , Let $\"\"$ .

$\"\"$ .

$\"\"$

Therefore, series is convergent when $\"\"$ .

$\"\"$ .

Interval of convergence is $\"\"$ .

$\"\"$

Power series representation of the function is $\"\"$ and

Interval of convergence is $\"\"$ .