Try finding the Taylor series first...

Assume that can be expressed as a polynomial.

Then .

By letting we see that .

Take the derivative of both sides

.

By letting we see that .

Take the derivative of both sides

.

By letting we see that and so .

Take the derivative of both sides

.

By letting we see that , so .

Take the derivative of both sides

By letting we see that and so .

You should be able to see that if we were to keep going we would have

.

Can you find for which values of that this series will converge for?

Hint: A geometric series converges for ...