1 − 1 + 2 − 6 + 24 − 120 + ⋯
Okay kiddo, let’s talk about something called “1 − 1 + 2 − 6 + 24 − 120 + ⋯”. It’s a really weird math problem that seems like it goes on forever. But don’t worry, we can explain it in a way you’ll understand.
First, we should learn what the “dots” mean. You know how when you count you say 1, 2, 3, 4…? Well, sometimes instead of writing it all out, we use a dot dot dot (…) to show that the numbers keep going. It’s like an abbreviation for “and so on”.
Now, let’s look at the numbers in this problem. They’re pretty different from each other, right? One goes up, then down, then up… it’s kind of confusing. But let’s take a closer look at the pattern.
The first number is 1. Then, we subtract 1 from it, which makes it 0. Then, we add 2 to that, which makes it 2. Then, we subtract 6 from that, which makes it -4. Finally, we add 24 to that, which makes it 20. Do you see the pattern?
Every time, we’re either subtracting or adding a bigger number than before. That’s why the whole thing seems to go up and down! It’s like a rollercoaster, going up and down and up and down.
Now, you might be wondering why we’re doing this weird pattern at all. Well, people who study math like to do these kinds of things just to see what happens. And it turns out that if we keep doing this pattern, the final answer is not really a set number… it’s kind of in between two numbers.
So, in other words, this problem doesn’t have just one right answer. Depending on how you look at it, the answer could be a little bit different. That’s why it’s so tricky!
But don’t worry about that too much. The important thing is that you understand how the numbers are changing, and why it’s such a strange problem. Maybe someday when you’re bigger you’ll understand it even better!
First, we should learn what the “dots” mean. You know how when you count you say 1, 2, 3, 4…? Well, sometimes instead of writing it all out, we use a dot dot dot (…) to show that the numbers keep going. It’s like an abbreviation for “and so on”.
Now, let’s look at the numbers in this problem. They’re pretty different from each other, right? One goes up, then down, then up… it’s kind of confusing. But let’s take a closer look at the pattern.
The first number is 1. Then, we subtract 1 from it, which makes it 0. Then, we add 2 to that, which makes it 2. Then, we subtract 6 from that, which makes it -4. Finally, we add 24 to that, which makes it 20. Do you see the pattern?
Every time, we’re either subtracting or adding a bigger number than before. That’s why the whole thing seems to go up and down! It’s like a rollercoaster, going up and down and up and down.
Now, you might be wondering why we’re doing this weird pattern at all. Well, people who study math like to do these kinds of things just to see what happens. And it turns out that if we keep doing this pattern, the final answer is not really a set number… it’s kind of in between two numbers.
So, in other words, this problem doesn’t have just one right answer. Depending on how you look at it, the answer could be a little bit different. That’s why it’s so tricky!
But don’t worry about that too much. The important thing is that you understand how the numbers are changing, and why it’s such a strange problem. Maybe someday when you’re bigger you’ll understand it even better!
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