Question Detail
Question
Prove by induction that 1² + 3² + 5² + ... + (2n-1)² = n(2n-1)(2n+1)/3 for n ≥ 1.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Base case n=1: 1² = 1(1)(3)/3=1 ✔. Assume n=k, sum for n=k+1 adds (2k+1)² → factorization yields formula ✔.
Hint
Add next square and factor.