How do I construct a proof by induction?

There are typically 4 steps: proving the base case, making an assumption, making the inductive step and finally concluding the proof.

The base case consists of proving that a statement is true for n = 1, the assumption to make is that the statement holds true for n = k, the trickiest part is the inductive step which is proving that the statement is true for n = k + 1 as long as it is true for n = k, and finally the simplest part is wrapping up the proof with a concise statement.

An example of a statement to prove is that n^3 + 2n is always divisible by 3 which I can go through using the whiteboard if needed.

AF
Answered by Alex F. Further Mathematics tutor

3158 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Solve the second order differential equation d^2y/dx^2 - 4dy/dx + 5y = 15cos(x), given that when x = 0, y = 1 and when x = 0, dy/dx = 0


Why does matrix multiplication seem so unintuitive and weird?!


Prove that sum(k) from 0 to n is n(n+1)/2, by induction


How do I find the square root of a complex number?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning