NSW Y12 Maths - Extension 2 Proof Induction: Series

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NSW Syllabus Reference: MEX-P2 Further Proof by Mathematical Induction

This NSW syllabus reference for Induction: Series focuses on

prove results using mathematical induction where the initial value of is greater than 1, and/or \(n\) does not increase strictly by 1, for example prove that \(n^2+2n\) is a multiple of 8 if \(n\) is an even positive integer
understand and use sigma notation to prove results for sums, for example: \(\sum\limits_{n = 1}^N {\dfrac{1}{{(2n + 1)(2n - 1)}} = \dfrac{N}{{2N + 1}}} \)
understand and prove results using mathematical induction, including inequalities and results in algebra, calculus, probability and geometry
use mathematical induction to prove first-order recursive formulae