$\"\"$ \ \

The function is $\"\"$ . \ \

Divide the numerator and denominator by $\"\"$ . \ \

$\"\"$ \ \

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

$\"\"$ \ \

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

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 $\"\"$ . \ \