Question Detail
Question
Prove by induction that 1³ + 2³ + 3³ + ... + n³ = (1+2+...+n)² for all n ≥ 1.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Base case n=1: 1³=1=(1)² ✔. Assume true for n=k: 1³+...+k³ = (1+...+k)². For n=k+1: sum = (1+...+k)² + (k+1)³ = (k(k+1)/2 + (k+1))² = ((k+1)(k/2 +1))² = ((k+1)(k+2)/2)² ✔.
Hint
Use previous sum and add (k+1)³, then factor.