Induction – Identities & Other

Proof by mathematical induction for identities and other results is part of the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). This subtopic applies mathematical induction to a broad mix of results: trigonometric products and sums, formulas for the \(n\)th derivative of a function, products of many factors, and the binomial theorem itself.

Students and teachers will cover how to adapt the induction structure to each type of result — including sequences built from earlier terms and claims about integers — extending the technique well beyond simple sums in the HSC Extension 2 course.