Answer: (n+2)2ⁿ⁻¹.
- A (n+2)2ⁿ⁻¹
- B (n+1)2ⁿ
- C n2ⁿ
- D 2ⁿ⁺¹
Correct answer: A. (n+2)2ⁿ⁻¹
Explanation: Sum = (n+1)2n-1 + 2n-1. Actually: C0+2C1+...+(n+1)Cn = sum(r=0 to n) (r+1)Cr = sum(r+1)nCr = n*2n-1+2n = (n+2)*2n-1.
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