Answer: 2n−1(n + 2).
- A 2n−1(n + 2)
- B 2ⁿ(n + 1)
- C n·2ⁿ
- D (n + 2)2ⁿ
Correct answer: A. 2n−1(n + 2)
Explanation: Σ(r+1)C(n,r) = n·2n−1 + 2ⁿ = 2n−1(n + 2).
Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.
Concept context
Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term