$\"\"$

Consider the power series is $\"\"$ .

The series is centered around $\"\"$ .

Its radius of convergence is $\"\"$ .

The radius of the convergence is $\"\"$ , then $\"\"$ must be $\"\"$ because $\"\"$ .

Since $\"\"$ should be $\"\"$ , for some fixed point $\"\"$ .

That is not possible since $\"\"$ .

It is not possible to find the power series with radius of convergence $\"\"$ .

$\"\"$

It is not possible to find the power series with radius of convergence $\"\"$ .