Answer: all values up to k.
- A all values up to k
- B only the value k
- C only the value 1
- D no values at all
Correct answer: A. all values up to k
Explanation: Strong induction assumes P(1), P(2), …, P(k) to prove P(k + 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.