Suppose that you want to show something is true for all positive integers. You could start by checking that the statement is true for \(n = 1\) , \(n = 2\) , and so on, but you would have to stop somewhere. Even if you check lots and lots of integers, you can run into problems. In such a case, mathematicians try not to end a proof with the words “and so on...” or “and so forth.” Instead, we use a principle called mathematical induction. We’ll discuss two forms of the principle. You’ll also be able to prove the binomial theorem in one of the problems.