Answer: 2ⁿ⁻¹.
- A 2ⁿ
- B n
- C 2ⁿ⁻¹
- D 2ⁿ⁻²
Correct answer: C. 2ⁿ⁻¹
Explanation: Sum of even-indexed binomial coefficients = 2<sup>n-1</sup>. This follows from adding (1+1)<sup>n</sup> and (1-1)<sup>n</sup> then halving.
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