Answer: That 13 - 1 = 0 is divisible by 6.
- A That (k+1)3 - (k+1) is divisible by 6
- B That 13 - 1 = 0 is divisible by 6
- C That n is even
- D That n3 is divisible by 6
Correct answer: B. That 13 - 1 = 0 is divisible by 6
Explanation: The base case checks n=1: 13 - 1 = 0, and 0 is divisible by 6 (0 = 6 x 0), so the base case holds.
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.