Prove that: $$\sum _{k=0}^{n}{{(-1)}^{k}\binom n k}=0$$
I tried with induction and failed.
A solution explain would be greatly appreciated.
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$\begingroup$ There are many solutions at the link in my comment above. $\endgroup$ – Potato Jul 8 '13 at 16:42
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The Binomial Theorem says $$(a+b)^n=\sum_{0\le r\le n}\binom nr a^{n-r}b^r$$
for real or complex $a, b$, and non-negative integer $n$.
Put $a=1,b=-1$
answered Jul 8 '13 at 16:42
