$\"\"$

The function is $\"\"$ .

Consider $\"\"$ .

This is sum of infinite series with $\"\"$ and common ratio $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

Find the interval of convergenceof $\"\"$ .

The above series is a geometric series with common ratio $\"\"$ .

Geometric series is convergent when common ratio $\"\"$ .

Therefore, the series is convergent if $\"\"$ .

$\"\"$

Interval of convergence is $\"\"$ .

$\"\"$

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

Interval of convergence is $\"\"$ .