Pascal’s triangle proof

Question

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?

@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

score 0 · Answer 1 · answered Feb 28 '18 at 12:38

0

$$ 0 = (-1+1)^n = \sum_{k=0}^n {n\choose k} (-1)^k 1^{n-k} = \sum_{k=0}^n {n\choose k} (-1)^k. $$

answered Feb 28 '18 at 12:38

Cettt

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Pascal’s triangle proof

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