First, some background.The number of natural numbers (1, 2, 3, 4, …) and the number of integers (…, -2, -1, 0, 1, 2, …) are both infinite. But are they the same kind of infinite?The answer is yes, because you can match each integer to a natural number. Order the integers like this:0, 1, -1,…

Let’s say we have a sequence, and we want to guess what polynomial generated it.For example:3, 10, 19, 30, 43, 58, 75, …Finite differences helps with determining that. How it works is, take the difference between each pair of terms.10 – 3 = 7, then 19 – 10 = 9, then 30 – 19 =…