Answer: 2ⁿ.
- A n
- B n!
- C 2ⁿ
- D 2ⁿ⁻¹
Correct answer: C. 2ⁿ
Explanation: Put x = 1: (1+1)<sup>n</sup> = 2<sup>n</sup> = nC<sub>0</sub> + nC<sub>1</sub> + ... + nCn. Sum of all binomial coefficients = 2<sup>n.</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