Answer: 6.
- A 4
- B 5
- C 6
- D 9
Correct answer: C. 6
Explanation: n³ − n = (n−1)n(n+1) is a product of three consecutive integers, always divisible by 6.
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.