Induction By Contradiction

So for years I used Proof By Induction, but never really understood why it worked. This frustrated me, and so I set out to discover the “proof” for proof by induction. I searched far and wide in all my textbooks and just kept finding the domino analogy to justify the three steps. Sure the analogy is cute but to me it never seemed like a proof. So after looking up induction in nearly every book I have, I found a decent explanation in Paul Foerster's Precalculus. He uses Proof By Contradiction to develop induction and the method is both clear and logical. Unfortunately this great induction lesson has been relegated to an appendix in the book with no exercises at all (particularly unfortunate since Foerster's claim to fame is his problem sets). Anyhow I used it to create a lesson, along with problems, that I have attached below: Here is the Pages '09 File: Induction 1.pages