Using Binomial Theorem for proofs.

Question

I need to prove that:

$$0 = \sum_{k=0}^n\binom{n}{k}(−1)^k$$

Any ideas, please?

Expand $(1+(-1))^n$ using the Binomial Theorem. Equivalently, expand $(1+x)^n$ and set $x=-1$. — André Nicolas, Feb 24 '15 at 19:46

score 0 · Accepted Answer · answered Feb 24 '15 at 19:48

0

Hint

By Binomial theorem, $$(a+b)^n=\sum_{k=0}^n\binom{n}{k}a^kb^{n-k}.$$

Set $a=-1$ and $b=1$ to get the result.

answered Feb 24 '15 at 19:48

Surb

1 Answers1