Answer: 10.
- A 9
- B 10
- C 12
- D 15
Correct answer: B. 10
Explanation: Even power 2n has (2n+1) terms; unique middle term is T(n+1)=C(2n,n)·xⁿ·(1/x)<sup>n</sup>=C(2n,n). Set C(2n,n)=184756. Trial n=10: C(20,10)=184756 ✓ (known value). Answer: n=10.
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