Induction – Series

Proof by mathematical induction for series is part of the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). Building on the induction met in Extension 1, this subtopic proves closed-form results for sums — from familiar arithmetic and geometric patterns to series with powers, trigonometric and inverse-trigonometric terms.

Students and teachers will cover how to set out the base case, state the inductive hypothesis, prove the inductive step and write the concluding statement examiners expect — applied to the harder summation results met in the HSC Extension 2 course.