## Example: A Proof by Induction

By |2017-01-01T15:25:37-08:00September 22nd, 2016|Categories: Courses, Math 341|Tags: |

You may comfortable with the logic of mathematical induction, but still feel uncomfortable with how to actually write up the proof. So here is an example taken from class today, presented in several different ways. Let's prove the following: Claim. For every integer $n\geq 1$ the following equality holds: $$\sum_{i=1}^n (2i-1)= n^2.$$ In other words, we [...]