Induction – Recursive Formulas & Calculus Results

Induction with recursive formulas and calculus is part of the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). Here induction proves facts about sequences where each term is built from the one before, such as \(u_{n+1}=3u_n+2^n\), and general formulas for repeated derivatives or integrals.

Students and teachers will cover how to check the first case, use the assumed case inside the recurrence or the next derivative, and reach a formula, bound or ordering for every \(n\) — a demanding part of induction in the HSC Extension 2 course.