This is an interactive website to help you learn how to write an induction proof. You should try to prove the statement yourself, and use the information on this webpage to check your work or to get a hint if you need one.

We will prove an equality. You will prove the similar equalities in your homework.
**You can see that most of the proof is missing.**
Click on any box to reveal the next step.

But * before you click*, try to write the proof yourself and figure out what will appear!

If you wish to make the text disappear again, refresh the page.

*Prove that \(1^2 + 2^2 + 3^2 + \dots + n^2 = \tfrac{1}{6}(n(n+1)(2n+1))\) for all \(n \in \mathbb N.\)*

*Proof:* We can see that and , so assume that . Continuing, we compute

Thus \(1^2 + 2^2 + 3^2 + \dots + n^2 = \tfrac{1}{6}(n(n+1)(2n+1))\) for all \(n \in \mathbb N.\)

We can also begin with the induction assumption (after the basis step of course!) and continue with valid operations.

*Proof:* We can see that and , so assume that . Continuing, we compute

Thus \(1^2 + 2^2 + 3^2 + \dots + n^2 = \tfrac{1}{6}(n(n+1)(2n+1))\) for all \(n \in \mathbb N.\)