The Formula for 1+2+3+4+5 to 1000
Have you ever wondered how to calculate the sum of consecutive numbers from 1 to 1000? Well, you're in luck because there's a formula for that!
The Formula
The formula to calculate the sum of consecutive numbers from 1 to n is:
1 + 2 + 3 + ... + n = n(n+1)/2
Where n is the last number in the sequence.
How it Works
Let's break down the formula and see how it works.
- n: This is the last number in the sequence. For example, if we want to calculate the sum of numbers from 1 to 1000, then n = 1000.
- n+1: This is the number that comes after n. In our example, n+1 = 1001.
- n(n+1): This is the product of n and n+1. In our example, n(n+1) = 1000 * 1001 = 1,001,000.
- /2: Finally, we divide the product by 2 to get the sum of the sequence.
Example: 1+2+3+4+5 to 1000
Let's use the formula to calculate the sum of numbers from 1 to 1000:
1 + 2 + 3 + ... + 1000 = 1000(1001)/2
= 500,500
So, the sum of numbers from 1 to 1000 is 500,500.
Conclusion
The formula for calculating the sum of consecutive numbers from 1 to n is a powerful tool that can save you a lot of time and effort. Whether you're a student, a teacher, or just a math enthusiast, this formula is an essential tool to have in your toolkit.
