Mathematical induction

problem

One Basket or Group Photo

Age

7 to 18

Challenge level

Libby Jared helped to set up NRICH and this is one of her favourite problems. It's a problem suitable for a wide age range and best tackled practically.
problem

Walkabout

Age

14 to 16

Challenge level

A walk is made up of diagonal steps from left to right, starting at the origin and ending on the x-axis. How many paths are there for 4 steps, for 6 steps, for 8 steps?
problem

Obviously?

Age

14 to 18

Challenge level

Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.
problem

Dirisibly Yours

Age

16 to 18

Challenge level

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.
problem

Farey Fibonacci

Age

16 to 18

Challenge level

Investigate Farey sequences of ratios of Fibonacci numbers.
problem

Ok! Now Prove It

Age

16 to 18

Challenge level

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?
problem

Binary Squares

Age

16 to 18

Challenge level

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?
problem

Farey Neighbours

Age

16 to 18

Challenge level

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?
problem

Particularly General

Age

16 to 18

Challenge level

By proving these particular identities, prove the existence of general cases.
article
An Introduction to Mathematical Induction

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