Trying without success to solve the following: what is the sum of $\binom{80}{0}-\binom{80}{1}+\binom{80}{2}-\binom{80}{3}...-\binom{80}{79}+\binom{80}{80}$
any help will be greatly appreciated
2026-04-25 15:07:40.1777129660
sum of a binomial coefficient
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The binomial coefficients are the 80th (or 81st?) row of Pascal's triangle. Each is the sum of the 2 numbers above it (with 0's above the extremal elements.
Therefore, each number in the row above contributes equally to the positive and negative expressions of this number, so the total is 0.