Question Detail
Question
Prove by induction that sum_{i=1}^n i(i+1)(i+2) = n(n+1)(n+2)(n+3)/4 for n ≥ 1.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Base case n=1: 1×2×3=6 = 1×2×3×4/4=6 ✔. Assume true for n=k, sum for n=k+1 adds (k+1)(k+2)(k+3) → factorization yields formula ✔.
Hint
Check base case, add next term, factorize.