Binomial sumHardQuestion 280011
Question
ⁿC₀ − ⁿC₁ + ⁿC₂ − ... + (−1)ⁿ ⁿCₙ equals:
- A0Correct
- B2ⁿ
- C1
- Dn!
Correct answer
0
Explanation
Setting x = −1 in (1+x)ⁿ = Σ ⁿCᵣ xʳ: (1+(−1))ⁿ = 0 = ⁿC₀ − ⁿC₁ + ⁿC₂ − ... Thus the alternating sum of binomial coefficients is 0 (for n ≥ 1).