SME
Grade 12 Math
Mathematical induction
The main lesson, then each kind of problem it solves.
Mathematical induction
Main lesson
The sum of odd numbers
Use this for “Prove 1 + 3 + 5 + … + (2n − 1) = n² by induction.”
A geometric sum
Use this for “Prove 1 + 2 + 4 + … + 2ⁿ⁻¹ = 2ⁿ − 1 by induction” (r = 2), or any ratio r.
The sum of squares
Use this for “Prove 1² + 2² + … + n² = n(n + 1)(2n + 1)/6 by induction.”
A divisibility proof
Use this for “Prove that n³ − n is divisible by 3 for every whole number n ≥ 1.”
The steps of a proof by induction
Use this for “Prove by induction that 1 + 3 + 5 + … + (2n − 1) = n² for every n ≥ 1.”