$\"\"$ \ \

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

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

$\"\"$ \ \

The power series is $\"\"$ . \ \

$\"\"$ . \ \

$\"\"$ \ \

$\"\"$ . \ \

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 $\"\"$ .