Answer: mathematical induction.
- A mathematical induction
- B checking a few cases
- C differentiating it
- D drawing a graph
Correct answer: A. mathematical induction
Explanation: Only induction guarantees a statement for all positive integers, not merely the cases tested.
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.