What does Pascal's Identity state regarding binomial combinations C(n, k)?
Answer and explanation
Correct answer: D. C(n, k) + C(n, k - 1) = C(n + 1, k), the recurrence forming Pascal's triangle
- Step 1: Pascal's identity states that any entry in Pascal's triangle is the sum of the two entries directly above it. Step 2. Algebraically: n! / (k!(n-k)!) + n! / ((k-1)!(n-k+1)!) = (n+1)! / (k!(n+1-k)!). Answer: C(n, k) + C(n, k - 1) = C(n + 1, k), the recurrence forming Pascal's triangle. Why not the others: It underpins the inductive proof of the Binomial Theorem.
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