STEP Prep Module 9

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STEP Prep Module 9

Proof by induction is a really useful way of proving results about the natural numbers. If you haven't met this powerful technique before, this module will introduce you to the idea and method of induction. If you're already familiar, check out some of the problems and STEP questions that can be answered in this way!
An Introduction to Mathematical Induction link

An Introduction to Mathematical Induction 

Stage: 5

This article gives an introduction to mathematical induction, a powerful method of mathematical proof.

Some Induction Examples link

Some Induction Examples 

Stage: 5

Some statements which can be proved using induction, and some example proofs.

Dirisibly Yours link

Dirisibly Yours 

Stage: 5 Challenge Level: Challenge Level:1

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.

Tens link

Tens 

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

STEP Induction Questions link

STEP Induction Questions 

Stage: 5

Some STEP questions that can be solved using induction, and a worked example.