$\"\"$

The function is $\"\"$ where $\"\"$ for all $\"\"$ .

Consider $\"\"$ .

$\"\"$

By using the standard geomentric summation :

$\"\"$

Generally for the most geomentric series the convergence radius is $\"\"$ , therefore the radius of convergence is $\"\"$ and with the interval of convergence $\"\"$ .

$\"\"$

$\"\"$ with radius $\"\"$ .

The interval of convergence $\"\"$ .