Induction – Divisibility

Proof by mathematical induction for divisibility is part of the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). This subtopic uses mathematical induction to prove that an expression is divisible by a given integer for every positive integer \(n\).

Students and teachers will cover how to set up the base case, assume the inductive hypothesis, and rearrange the inductive step so the required divisibility is clear — a frequently examined application of induction in the HSC Extension 2 course.