Answer: the inductive hypothesis.
- A the inductive hypothesis
- B just the base case
- C a final guessed value
- D a random chosen number
Correct answer: A. the inductive hypothesis
Explanation: The inductive hypothesis about the k case is rewritten to reveal the divisor in the (k + 1) 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.