Question Detail
Question
Prove by mathematical induction that 1 + 2 + 3 + ... + n = n(n+1)/2 for all n ≥ 1.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Base case: n=1 → 1 = 1(1+1)/2 =1 ✔. Assume true for n=k: 1+2+...+k = k(k+1)/2. For n=k+1: 1+2+...+k+(k+1) = k(k+1)/2 + (k+1) = (k+1)(k/2 + 1) = (k+1)(k+2)/2 ✔.
Hint
Check base case, assume for k, prove for k+1.