Answer: n².
- A n(n + 1)
- B n²
- C n(n + 1)/2
- D 2n
Correct answer: B. n²
Explanation: The sum of the first n odd numbers is n².
Mathematical induction works like a row of dominoes: proving the base case P(1) tips the first domino, and proving the inductive step (P(k) ⟹ P(k+1)) guarantees each domino knocks over the next - together these two facts guarantee ALL dominoes fall, without checking each one individually.
Concept context
A proof technique used to establish that a statement is true for every natural number, using a base case and an inductive step.