Question Detail
Question
Prove by induction that 1×3 + 3×5 + 5×7 + ... + (2n-1)(2n+1) = n(2n+1)(2n+3)/3 for n ≥ 1.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Base case n=1: 1×3 = 1(3)(5)/3 =5 ✔. Assume true for n=k, then sum for n=k+1 adds (2k+1)(2k+3) → factorization yields formula ✔.
Hint
Add next term (2k+1)(2k+3) and factor.