Proof

0 covered of 6 dot points

Lessons

Nothing written for this module yet. The dot points are listed beside this, so you can still see exactly what the module asks of you and take it to the official syllabus.

What the syllabus asks

ME-P1 Proof by Mathematical Induction

understand the nature of inductive proof, including the ‘initial statement’ and the inductive step (ACMSM064)ACMSM064
not written yet
prove results using mathematical induction
not written yet · needs a worked example
- prove results for sums, for example $1 + 4 + 9 + \dots + n^{2} = \frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ for any positive integer $n$ (ACMSM065)ACMSM065
  not written yet · needs a worked example
- prove divisibility results, for example $3^{2 n} - 1$ is divisible by 8 for any positive integer $n$ (ACMSM066)ACMSM066
  not written yet · needs a worked example
identify errors in false ‘proofs by induction’, such as cases where only one of the required two steps of a proof by induction is true, and understand that this means that the statement has not been proved
not written yet · needs a worked example
recognise situations where proof by mathematical induction is not appropriate
not written yet

Wording is the official syllabus, read from the NESA document by a parser. The full document.