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The problem asks to calculate \( S_1 \), \( S_2 \), and \( S_3 \), where for all \( n \in \mathbb{N}^* \), we have:

\[
S_n = 1 + 2 + \cdots + n
\]

This is the sum of the first \( n \) natural numbers.

### Step-by-Step Calculation:

1. **For \( S_1 \):**
   \[
   S_1 = 1
   \]

2. **For \( S_2 \):**
   \[
   S_2 = 1 + 2 = 3
   \]

3. **For \( S_3 \):**
   \[
   S_3 = 1 + 2 + 3 = 6
   \]

Thus, the values are:
- \( S_1 = 1 \)
- \( S_2 = 3 \)
- \( S_3 = 6 \)

Would you like more details about the formula for the sum of the first \( n \) natural numbers, or any other clarification?

Here are five related questions:
1. How do we generalize the sum of the first \( n \) natural numbers?
2. What is the formula for \( S_n \) in terms of \( n \)?
3. Can this formula be extended to other types of sequences?
4. What is the relationship between \( S_n \) and triangular numbers?
5. How can you calculate \( S_n \) using induction?

**Tip:** The formula for the sum of the first \( n \) natural numbers is \( S_n = \frac{n(n+1)}{2} \).

Pour tout n ∈ N* on pose : S_n = 1 + 2 + ⋯ + n. Calculer S_1 ; S_2 et S_3

Learn how to calculate the sum of the first n natural numbers with this detailed guide. We explore how to compute S_1, S_2, and S_3, along with the formula for the sum of any n natural numbers. Suitable for students in Grades 5-7.

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