Prove that ∑ from k =1 to n of (-1)^k*k^2 = (-1)^n*((n(n+1)/2) for all positive integers n.

In words: Prove that the sum (from k =1 to n) of negative one to the k times k squared is equal to negative one to the n, times (n times (n plus 1), divided by 2.

I am beyond lost.