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

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

This is the well-known formula to calculate the sum of an arithmetic series where the first term is 1, the common difference is 1, and the number of terms is \( n \). The formula can be derived by recognizing the sequence as an arithmetic progression.

Would you like a step-by-step derivation or an explanation of how this formula works?

Here are five related questions to expand on this:
1. What is the formula for the sum of the first \( n \) squares?
2. How can you prove this formula using mathematical induction?
3. Can you derive the sum of the first \( n \) odd numbers?
4. How is this formula related to triangular numbers?
5. What is the formula for the sum of the first \( n \) terms of a geometric series?

**Tip:** The sum of the first \( n \) terms of an arithmetic series can be calculated even if the sequence does not start at 1; you just need the first term, the last term, and the number of terms!

What is 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 arithmetic progression concept is essential for understanding basic summation techniques. Suitable for students in Grades 6-8.

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