What is Mathematical Induction?

Mathematical induction is a type of direct proof, where you can prove sequences or series. A good example of this is that we can prove 1 + 3 + 5 + .... + (2n-1) = n^2. There are 4 steps: 1. Prove the first case, or the n=1 case for this example. 2. Assume that the k-th case is true for any positive integer number k. 3. Using the assumption, prove that the (k+1)-th case. For this example we take n = k+1. 4. So we've just proved that if the k-th case is true then the (k+1)-th case must be true! So if the 1st case is true, then the 2nd case must be true. Then since the 2nd case is true, so must the 3rd case. This logic carries on and therefore we have proved what we wanted to prove for all integers!

AH
Answered by Ayesha H. Maths tutor

3652 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Co-ordinate Geometry A-level: The equation of a circle is x^2+y^2+6x-2y-10=0, find the centre and radius of the circle, the co-ordinates of point(s) where y=2x-3 meets the circle and hence state what we can deduce about the relationship between them.


Use the substitution u=4x-1 to find the exact value of 1/4<int<1/2 ((5-2x)(4x-1)^1/3)dx


What are complex numbers?


Given that x=ln(t) and y=4t^3,a) find an expression for dy/dx, b)and the value of t when d2y/dx2 =0.48. Give your answer to 2 decimal place.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences