Extension Proof – Mathematical induction

This lesson comprises two (2) master classes focusing on:

• Mathematical induction

Content:

ME-P1

• Understand the nature of inductive proof, including the ‘initial statement’ and the inductive step
• Prove results using mathematical induction
  • prove results for sums, for example \( 1+4+9+...+n^2=\frac{n(n+1)(2n+1)}{6} \) for any positive integer \( n \)
  • prove divisibility results, for example \( 3^{2n}−1 \) is divisible by 8 for any positive integer \( n \)
• 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
• Recognise situations where proof by mathematical induction is not appropriate