Answer: 2 > 1.
- A 2 > 1
- B 1 > 2
- C 2 = 1
- D 1 < 0
Correct answer: A. 2 > 1
Explanation: Substituting n=1: 2<sup>1</sup> = 2, and 2 > 1 is true, 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.