This is part of the HSC Mathematics Extension 1 course under the topic Proof by Mathematical Induction.
In this post, we will explore mathematical induction by understanding the nature of inductive proof, including the ‘initial statement’ and the inductive step. Mathematical induction is used as a general method to see if proofs or equations are true for a set of numbers in a quick way.
Mathematical induction has the following steps:
- State any assumptions
- Prove the equation true for k=1 (or whatever the starting number is)
- Prove true for k+1
- Finally, prove true all integers in the set.
- A concluding statement stating if the proof was true or not.
Introduction to Mathematical Induction