Find an expression for the general term of the series below. Assume the starting value of the index,k, is 0. Denote terms such ask! or (2k)! as fact_k or fact_2k. Here is the series...

$\displaystyle (x-8)^4 - \frac{(x-8)^6}{2!} + \frac{(x-8)^8}{4!} - \frac{(x-8)^10}{6!} + ...$

What I get for an answer is ((-1)^(k+2)(x-a)^(2k+4))/(fact_(k+1)).

What I am wondering is why is this wrong? Any help appreciated.