is correct, but it is not in the form .
i am to use
to find a power series representation for
additionally I need to find the interval of convergence.
since,
and
then
the book says is a power series representation of the original function can someone point out my error?
we'll i don't think i can use the distributive property to make it
since this is basically an polynomial of infinitely many terms being multiplied by a binomial.
i don't really see anything to do here.
This depends on the level of rigor with which you need to "find" the series for . Do you need an accurate proof that it converges to the function inside the interval of convergence? I agree that infinite sums require special care, but using distributivity in the way you did is fine as the first approximation.