Answer: 0.
- A 2ⁿ
- B 2ⁿ⁻¹
- C 1
- D 0
Correct answer: D. 0
Explanation: Put x = -1 in (1+x)n: (1-1)n = 0 = nC0 - nC1 + nC2 - .... So the alternating sum = 0.
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