My name is Christopher, and over the course of the last two months, our math class has been heavily diving into proofs. We’ve learned many different proof methods, but one of the ones that have stuck out to me the most is induction. It’s very amazing to me how we can say just for N to be true, then N+1 must also be true, and plug N+1 to show that it’s true. So today, I decided to show the induction proof for sum of n squares that I learned recently.

The sum of all squares is known for being a very widely proofed theorem, with ways of proving it ranging from derivation to visual proofs, there are many diverse ways to prove. Today, I decided to use induction to prove the Sum of n squares. Firstly, for induction to work, I had to assume that the formula is true and works for any number. However, if this is true, then it must also be true that n+1 is also true. In order to test this, we add n+1 to the original equation and then expand the formula. After expanding, factor the expanded equation. One interesting technique to factor the expanded equation is by using synthetic division, where we assume that n+1 since it replaces n during induction. If the expanded formula is factored, then it implies that induction was successful. After obtaining the factored form, analyze it for n+1 in the places of the original formula’s n. By showing that n+1replaces n in this equation, we have successfully used induction to prove sum of all n squares. I believe that induction is a very powerful way to prove a theorem, and I hope to spread awareness on it so that more people are able to see the wonder and in mathematics.