(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: A little help with a binomial theorem proof

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