Math 331: Lecture 2 Inequality,Induction, Power Sums

Steven starts off with the inequality .
The main idea is how to probe when you encounter such inequality. For example its easy to see that there is some symmetry here. All the variables appear exactly the same number of times. So one way to probe is either with or make all variables the same, let’s say and one gets on both the sides. The other way to think about is the dimension idea and if one uses meters, one finds that its is or volume on both the sides.

The induction problem was about everyone has the same name.

Power Sums is the idea that one can derive the sum of the powers from the previous sums.