Every power series has a interval convergence of the form .

Where is a constant real number and which is center of convergence.

In addition the end points may or may not be induced.

For the interval the convergence is to be .

Compare the interval with .

Here or .

.

The radius of the convergence but there is no possibility that the value of center of convergence is .

Because is a constant real number.

Therefore there cannot be a power series whose interval of convergence .

No, It is not possible to find a power series whose interval of convergence is .

No, It is not possible to find a power series whose interval of convergence is .