The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
Notes [Warning: Example 3 is no longer in specification]
Topic assessment (with solutions)
Note: Q4 is no longer in the specification. Use your knowledge of proof by induction to figure out how to construct a proof for recurrence relations.
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
Topic videos:
Using induction to prove results about divisibility [Note: This video uses a slightly different method to those discussed in class]
Extra fun examples [These problems go beyond what you would be expected to prove in an exam]
Extra fun! Some more tidbits on divisibility:
One of the most groundbreaking (and earth-shattering) results in mathematics: