- #1
bennyska
- 112
- 0
Homework Statement
(here, (n,k) reads n choose k)
prove that (n,0) - (n, 1) + ... + (-1)n(n,n) = 0
Homework Equations
binomial theorem
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!