1+2+3+4+5+6 To 100 Formula

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Jun 15, 2024

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The Formula for 1+2+3+4+5+6 to 100

Have you ever wondered how to calculate the sum of consecutive integers from 1 to 100? Well, you're in luck because there's a simple formula to do just that!

The Formula

The formula to calculate the sum of consecutive integers from 1 to n is:

1 + 2 + 3 + ... + n = n(n+1)/2

This formula is known as the formula for the sum of an arithmetic series.

How it Works

Let's break down how this formula works:

• n represents the last number in the sequence. For example, if you want to calculate the sum of 1+2+3+...+100, then n is 100.
• n+1 represents the number of terms in the sequence. In this case, there are 100 terms in the sequence.
• n(n+1)/2 calculates the sum of the sequence.

Example: Calculating 1+2+3+...+100

Using the formula, let's calculate the sum of 1+2+3+...+100:

1 + 2 + 3 + ... + 100 = 100(100+1)/2 = 100(101)/2 = 5050

So, the sum of 1+2+3+...+100 is 5050.

Conclusion

The formula for calculating the sum of consecutive integers from 1 to n is a powerful tool for quickly calculating large sums. Whether you're a student, teacher, or simply a math enthusiast, this formula is sure to come in handy.

So, the next time you need to calculate a large sum, remember: n(n+1)/2 is your friend!