1. The problem statement, all variables and given/known data (here, (n,k) reads n choose k) prove that (n,0) - (n, 1) + ... + (-1)n(n,n) = 0 2. Relevant equations binomial theorem 3. The attempt at a solution so this proof is relatively straightforward when n is odd. it's just matching up terms and having them cancel each other out. i'm having a problem proving it when n is even, because each term doesn't match up exactly. and the middle term also alternates between plus or minus depending on whether n/2 is even. (i think i have the middle term is (-1)n(n,n/2). but anyway, i've been having trouble with it. a little hint or two would be nice. gracias!