1
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ There are many solutions at the link in my comment above. $\endgroup$ – Potato Jul 8 '13 at 16:42
9
$\begingroup$

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 $a=1,b=-1$

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.