Proof by Mathematical Induction
Learn induction structure, divisibility proofs, and inequality proofs using clear base-case and inductive-step reasoning.
Active lessons
4
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Diagnostic
Take the topic test
A timed, ~60-minute test drawn at random across all 3 subtopics of this unit. You get a marked result, a predicted band, and a clear list of which subtopics to re-practise.
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
4 of 4 active
Lesson 1
Introduction to Mathematical Induction
Understand why induction works and prove the formula for the sum of the first n positive integers.
Lesson 2
Induction Divisibility Proofs
Use induction to prove divisibility results by exposing known multiples in the k + 1 step.
Lesson 3
Induction Inequality Proofs
Use induction to prove inequalities and choose the correct base case for the stated range.
Lesson 4
Prior Knowledge Revision: Induction
Activate prior knowledge for proof by induction: evaluate sigma notation sums using standard formulas, compute combinations C(n,r), apply Pascal's identity, and factor exponential expressions of the form A^(k+1) ± A^k.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.