How does proof by induction work?

Proof by induction is one of the most important mathematical methods. We take a statement we think is true for all integers n and prove that we're right:

We show something works in a trival, easy case (the base case). Often this is for n=1 or n=0.

Then we make our Induction hypothesis where we simply state that we're going assume our statement is true for some value n = k.

Then we show, often algebraically, that, given our hypothesis, our statement is true for n = k+1. This is the Induction step.

So then the statement is true for all integers bigger than our base case n. We've shown for example, that the base case n = 1 is true so n+1 = 2 must be true due to our induction step. And n = 3, 4, 5... and so for every single integer number.

Cordelia W. A Level Maths tutor, A Level Further Mathematics  tutor, ...

1 year ago

Answered by Cordelia, an A Level Further Mathematics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£24 /hr

Jaisal P.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Further Mathematics , Maths

Further Mathematics

“Hello, my name is Jaisal. I'm studying Maths at Durham University, and I'm here to help you improve your Maths. ”

£22 /hr

Matthew B.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Further Mathematics , Science+ 2 more

Further Mathematics

“About me: Hello! My name is Matt and I'm a 3rd year Maths student at the University of Warwick. I achieved all A*s at GCSE and 4 A*s at A-Level in Maths, Further Maths, Physics, and Chemistry. I am offering tutoring forA-Level Maths, ...”

£20 /hr

Shaun F.

Degree: Mathematics with International Study (Masters) - Exeter University

Subjects offered:Further Mathematics , Maths

Further Mathematics

“Hi, I'm Shaun! I'm currently studying for a masters in Mathematics at the University of Exeter..”

MyTutor guarantee

About the author

Cordelia W.

Currently unavailable: for new students

Degree: Mathematical Science (Masters) - Durham University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics

“I LOVE maths and believe I can pass on my love of the subject. I have been teaching maths and physics for years. I taught myself maths and physics, I helped my friends understand both subjects, I went on toteach a whole secondary scho...”

You may also like...

Posts by Cordelia

How do I expand out a pair of brackets?

How do I simplify surds?

How do stars like ours form and die?

How does proof by induction work?

Other A Level Further Mathematics questions

If a car of mass 1000kg travels up a slope inclined at 5 degrees at a speed of 20 meters per second calculate the power output of the car's engine (assuming a resistive force due to friction of 500N)

How do you prove by induction?

Integrate (x+4)/(x^2+2x+2)

What is a complex number?

View A Level Further Mathematics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss