Answer: nCr xʳ.
- A nCr
- B nCr x
- C nCr xʳ
- D nPr xʳ
Correct answer: C. nCr xʳ
Explanation: T(r+1) = nCr x 1<sup>n-r</sup> x x<sup>r</sup> = nCr x x<sup>r.</sup>
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