Answer: 1 = 1.
- A 1 = 1
- B 1 = 2
- C 2 = 1
- D 1 = 0
Correct answer: A. 1 = 1
Explanation: Substituting n=1: left side = 1, right side = 1(2)/2 = 1. So P(1) is 1 = 1, which is true.
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.