Induction homework

This work can be completed on paper from home and then brought into school on the first day of term. However, do not worry if you cannot attempt it or finish it in time for September as students will be given time at the start of term to complete it as well. Each subject area has created a virtual induction lesson, just for you.

Many students notice the step that makes an assumption, in which P (k) P ( k) is held as true. That step is absolutely fine if we can later prove it is true, which we do by proving the adjacent case of P (k + 1) P ( k + 1). All the steps follow the rules of logic and induction. Mathematical induction works if you meet three conditions:

If you can do that, you have used mathematical induction to prove that the property P P is true for any element, and therefore every element, in the infinite set. You have proven, mathematically, that everyone in the world loves puppies. Those simple steps in the puppy proof may seem like giant leaps, but they are not.

If you think you have the hang of it, here are two other mathematical induction problems to try: 1) The sum of the first n positive integers is equal to n (n + 1) 2 We are not going to give you every step, but here are some head-starts: Base Case: P (1) = 1 (1 + 1) 2 Is that true? Induction Step: Assume P (k) = k (k + 1) 2