Answer: n ≥ 5.
- A n ≥ 2
- B n ≥ 3
- C n ≥ 5
- D all n
Correct answer: C. n ≥ 5
Explanation: It fails at n = 2, 3, 4 but holds for n ≥ 5, which is the correct base case.
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.