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NSW Y12 Maths Standard 1 NSW Y12 Maths Standard 2 NSW Y12 Maths Advanced NSW Y12 Maths Extension 1 NSW Y12 Maths Extension 2

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Complex Numbers Proof Further Work With Vectors Integration Mechanics

NSW Y12 Maths - Extension 2 Proof Induction: Other

Resources for Induction: Other

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Proof Subtopics

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Language of Proof Methods of Proof Inequalities Proof Induction Series Induction Divisibility Induction Inequalities Induction Other Induction Recursive

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Videos relating to Induction: Other.

  • Induction Other - Video: Mathematical Induction: Other 1

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Syllabus Reference

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

This NSW syllabus reference for Induction: Other 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