Consider the theorem: "If n is even, then n + 1 is odd." In STEP 1, we completed Direct, Contraposition, and Contradiction Proofs of this theorem.

Let P(n) be "for all positive integers n, the integer immediately following the nth positive even integer is odd." Answer the following:

1. What is the benefit of writing P(n) in terms of the nth positive even integer instead of working with simply an n (even) and n+1 (odd) when we are attempting induction? 2. What would the Basis Step look like? What is the first n value: 1 or 2? 3. What do we assume to be true in the Inductive Step? 4. What are we trying to show to be true in the Inductive Step? 5. How is this different from the way we use Induction to prove Summation Formulae?