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There are **23** NRICH Mathematical resources connected to **Mathematical induction**, you may find related items under Patterns, sequences and structure.

Problem
Primary curriculum
Secondary curriculum
### Tens

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Converging Product

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Particularly General

By proving these particular identities, prove the existence of general cases.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Binomial Coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Farey Fibonacci

Investigate Farey sequences of ratios of Fibonacci numbers.

Age 16 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Farey Neighbours

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?

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Symmetric Tangles

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!

Age 14 to 16

Article
Primary curriculum
Secondary curriculum
### An Introduction to Mathematical Induction

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

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Fibonacci Fashion

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Fractions

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gosh Cosh

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Water Pistols

With n people anywhere in a field each shoots a water pistol at the nearest person. In general who gets wet? What difference does it make if n is odd or even?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Obviously?

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dirisibly Yours

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Counting Binary Ops

How many ways can the terms in an ordered list be combined by repeating a single binary operation. Show that for 4 terms there are 5 cases and find the number of cases for 5 terms and 6 terms.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Walkabout

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### One Basket or Group Photo

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.

Age 7 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Powers

You add 1 to the golden ratio to get its square. How do you find higher powers?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Binary Squares

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Growing

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### OK! Now Prove It

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

Age 16 to 18

Challenge Level