MYTUTOR SUBJECT ANSWERS

608 views

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, ...

2 years 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

87 SUBJECT SPECIALISTS

£36 /hr

James G.

Degree: Mathematical Physics (Doctorate) - Nottingham University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
.STEP.

“Currently a 3rd year PhD student in Mathematical Physics. I'm very passionate about teaching as well as my subject area. Look forward to hearing from you.”

£20 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Further Mathematics , Maths+ 3 more

Further Mathematics
Maths
.STEP.
.MAT.
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

£22 /hr

Max G.

Degree: Mathematics and Physics (Masters) - Durham University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics
Physics
Maths

“I am a maths and physics student at the University of Durham, for as long as I can remember i have been obsessed with all things science! I am patient, friendly and most of all understanding to the fact that the sciences aren't for ev...”

About the author

£22 /hr

Cordelia W.

Degree: Mathematical Science (Masters) - Durham University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics
Physics
Maths

“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

How to approximate the Binomial distribution to the Normal Distribution

What modules have you done before?

Find arsinh(x) in terms of x

Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

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

mtw:mercury1:status:ok