# Using Binomial Theorem to show that (-1)^k C(n,k) [duplicate]

I came across this question on my text book and i didn't know how to prove it.

Use the Binomial Theorem to show that $$0=\sum_{k=0}^n \ (-1)^ {k} C(n,k)$$

• $(x+y)^n = \sum_{k=o}^n C(n,k) x^k y^{n-k}$. Try $x=1, y=-1$. – Friedrich Nietzsche Feb 27 '14 at 12:33
• @FriedrichNietzsche: If that doesn't kill you, it will make you stronger; an ubermensch. – user99680 Feb 27 '14 at 13:04
• @FriedrichNietzsche : That should be moved to an answer – leonbloy Feb 27 '14 at 13:05