Proof by induction
Section overview:
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.
CP1-Chp8-ProofByInduction.pptx
Notes:
Notes [Warning: Example 3 is no longer in specification]
Summary questions:
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.
Extra resources:
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: