Answer: nC 1 a n-1 b.
- A nCn-1 a b<sup>n-1</sup>
- B n a<sup>n-1</sup> b²
- C nC<sub>2</sub> a<sup>n-2</sup> b²
- D nC<sub>1</sub> a<sup>n-1</sup> b
Correct answer: D. nC<sub>1</sub> a<sup>n-1</sup> b
Explanation: T<sub>2</sub> = T(1+1) = nC<sub>1</sub> a<sup>n-1</sup> b<sup>1</sup> = n a<sup>n-1</sup> b.
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