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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 $$ 0=\sum_{k=0}^n \ (-1)^ {k} C(n,k)$$

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