Answer: 2r.
- A r
- B 2r+1
- C 2r
- D r+2
Correct answer: C. 2r
Explanation: The rth term has coefficient C(n, r−1) and the (r+2)th term has coefficient C(n, r+1). Setting them equal: C(n, r−1) = C(n, r+1). Using the symmetry C(n,k) = C(n,n−k), this means r−1 = n−(r+1) = n−r−1, so 2r = n.
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