Answer: 512.
- A 256
- B 512
- C 1024
- D 511
Correct answer: B. 512
Explanation: The sum of even-indexed binomial coefficients equals 2<sup>n−1</sup> = 2⁹ = 512.
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