ELI5: Explain Like I'm 5

1 + 2 + 4 + 8 + · · ·

Okay kiddo, have you ever counted how many balls you have in your toy box? Yes? Great! Let's count together for a moment, 1, 2, 3, 4... But what if I told you that you could keep counting and the numbers would just keep getting bigger and bigger, forever and ever? That might seem silly, but it's actually true!

Now let's look at what happens when we add up 1, 2, 4, 8, and so on. This is a special sequence of numbers where each number is twice as big as the one before it. So, we start with 1. Then we add 2 to get 3. Then we add 4 to get 7. Then 8 to get 15. And we can just keep going on and on like that!

But what if we wanted to know what the total of all these numbers is? That's where things get really interesting. Even though we keep adding bigger and bigger numbers, we can actually figure out what the answer is! Do you remember how sometimes we count by skipping numbers? Like when we count by 2s, we say 2, 4, 6, 8... Well, there's a special trick we can use to figure out the total of 1, 2, 4, 8, and so on.

First, we start with 1. Then we double that number, and add it to the 1 we started with, which gives us 3. Then we double that number, and add it to the 3 from before. So we get 6. Then we double that number and add it to the 6 from before, which gives us 12. And we can keep going on like this forever, just like the counting we did before!

Now, you might be wondering what the point of all this is. Well, sometimes mathematicians like to study things that seem simple, just to see what happens. And this sequence of numbers - 1, 2, 4, 8, and so on - is actually really important in a lot of different parts of math. It's called a geometric series, and figuring out the total of all the numbers in the sequence helps us understand all sorts of things about how numbers work.

So there you have it, kiddo. We started with adding simple numbers together, but ended up exploring a really interesting concept in math. Keep counting and exploring, and you might just discover something new and exciting, too!