# Pascal’s triangle proof [duplicate]

Prove using the binomial theorem that alternately adding and subtracting elements across a row of Pascal’s triangle always results in zero.

I need help constituting a proof. I am able to show this works for specific cases and by substituting numbers into the binomial theorem but how will I go about a general proof that illustrates this works for every case?

## marked as duplicate by Parcly Taxel, drhab, Martin R, B. Goddard, GNUSupporter 8964民主女神 地下教會Feb 28 '18 at 12:46

• @Parcly Taxel Doesnt seem like a duplicate since OP has not found the link with $\sum_k \binom{n}{k} (-1)^k$ – krirkrirk Feb 28 '18 at 12:44
$$0 = (-1+1)^n = \sum_{k=0}^n {n\choose k} (-1)^k 1^{n-k} = \sum_{k=0}^n {n\choose k} (-1)^k.$$