Answer: Verify the base case, usually P(1).
- A Assume P(k) is true before checking anything else
- B Verify the base case, usually P(1)
- C Prove P(k+1) directly without a base case
- D Substitute n equal to infinity into the statement
Correct answer: B. Verify the base case, usually P(1)
Explanation: The first step (base case) checks that the statement is true for the smallest value of n, usually n = 1.
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.