Question Detail
Question
Prove by induction that 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6 for n ≥ 1.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Base case n=1: 1² = 1(2)(3)/6=1 ✔. Assume true for n=k. For n=k+1: sum = k(k+1)(2k+1)/6 + (k+1)² = (k+1)(k(2k+1)/6 + (k+1)) = (k+1)(k+2)(2k+3)/6 ✔.
Hint
Add the next term and factorize.