In this video, I’m going to work through five examples using mathematical induction. The first two examples involve summations, and the last three examples have an inequality. In each of these examples, I work through specials cases before wiring a proof so that you can get a feel for the result before actually proving the result holds using mathematical induction.
In this video, I’m going to cover three first examples using mathematical induction. So I’m going to assume that you have never seen mathematical induction before. So this is the first step, in a series of steps, to learn how to use and what mathematical induction is. Of course, to do that, we need to start with what the natural numbers are.
Many people have celebrated Euler’s Theorem, but its proof is much less traveled. In this article, I discuss many properties of Euler’s Totient function and reduced residue systems. As a result, the proof of Euler’s Theorem is more accessible. I also work through several examples of using Euler’s Theorem.