17: Using the undetermined coefficients approach you should get

There is no readily identifiable pattern to these numbers, so we leave it like this.
This method does not directly yield the region of validity of this expansion. Obviously it cannot work for x = −1, so the radius of convergence cannot be more than 1, experience suggests that it is also the correct answer.

Following the product approach you should get

Do not forget to specify the set of validity of this expansion.

Answer