1 − 1 + 2 − 6 + 24 − 120 + · · ·

Okay kiddo, do you know what adding numbers means? It's like putting things together to make a bigger thing! Well, mathematicians like to play games with these numbers.

This game is called a series, where you add up a bunch of numbers in a particular way. The series we're playing with here goes like this:

1 − 1 + 2 − 6 + 24 − 120 + · · ·

Isn't that funny looking? Well, we need to figure out what the pattern is so we can figure out the answer.

Let's start with adding the first two numbers, 1 and -1. What do you get? Zero! That's right, these two numbers cancel each other out.

Now let's add the first three numbers, 1, -1, and 2. What do you get? One!

Let's add the first four numbers now: 1, -1, 2, and -6. What do you get? -4!

Do you see a pattern yet? Every time we add a new number, it flips between positive and negative and gets bigger and bigger!

So, what's the answer to this series? Well, it doesn't have a real answer because it goes on forever. But if we add up a certain number of terms, we can get an approximation.

For example, if we add up the first four terms, we get -4. If we add up the first five terms, we get 20. If we add up the first six terms, we get -100.

It's a tricky game, but it helps us practice our math skills and understand patterns!