This is not an easy question.

Without the (-1)^j you can find the answer Summation - Wikipedia, the free encyclopedia

To figure out the answer you will probably need to use the same techniques.

Other than this I can only give you the hint that

is a polynomial of degree k+1, this means that you can find the closed formula by evaluating at k+2 points, and interpolating them (since there is a unique interpolating polynomial.)