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The image you've provided shows the formula for the sum of the first \( n \) natural numbers:

\[
1 + 2 + 3 + 4 + \dots + n = \frac{n(n + 1)}{2}
\]

This formula is used to calculate the sum of a sequence of consecutive integers starting from 1 up to \( n \). The formula can be derived by pairing the first and last terms of the sequence, continuing inward, and recognizing that each pair sums to the same value.

### Do you have any questions or would you like more details?
Here are some related questions to deepen your understanding:

1. How would you prove the formula for the sum of the first \( n \) natural numbers using mathematical induction?
2. What is the sum of the first 100 natural numbers?
3. How does this formula relate to the concept of arithmetic series?
4. Can this formula be used to find the sum of an arithmetic series that doesn't start with 1?
5. How would the formula change if the series was the sum of the first \( n \) odd numbers?

**Tip:** When solving problems involving sequences, it's useful to recognize whether the sequence is arithmetic, geometric, or another type, as this will guide the choice of formula to use.

What is the formula for the sum of the first n natural numbers?

Learn how to calculate the sum of the first n natural numbers using the formula S = n(n + 1) / 2. This problem covers key concepts in arithmetic series and is suitable for students in Grades 6-8.

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