How to Prove the Following Sum is Zero

Question

How to prove that $\sum_{x=0}^{n}$ $(-1)^x$$ n \choose x$ = $0$. I know there is a connection to the binomial expansion, but I am having difficulty formalizing it with all the notation.

Possible duplicate of Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$ — Martin R, May 30 '19 at 01:56
Also: https://math.stackexchange.com/q/94514/42969, https://math.stackexchange.com/q/879032/42969 — Martin R, May 30 '19 at 01:57

score 7 · Answer 1 · answered May 30 '19 at 01:17

7

$\displaystyle \sum_{x=0}^n {n \choose x}y^x=(1+y)^n$.

Put $y=-1$.

answered May 30 '19 at 01:17

CY Aries

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How to Prove the Following Sum is Zero

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