https://file.aiquickdraw.com/mathbot/file/1725467154546kt99hvh4.jpg

The image presents an algorithm in Python, followed by an instruction to execute it for \( N = 4 \) and fill in the corresponding table based on the outputs.

Here is the provided algorithm in text form:

```python
S = 0
N = int(input("Entrez la valeur de N : "))

for i in range(0, N - 1):
    S = S + 1 + i + 3

print(S)
```

Given \( N = 4 \), we can analyze and determine the values for each step:

1. **Initial Setup**: \( S = 0 \), \( N = 4 \).

2. **Loop Execution**:
    - **Step 1**: \( i = 0 \): \( S = 0 + 1 + 0 + 3 = 4 \)
    - **Step 2**: \( i = 1 \): \( S = 4 + 1 + 1 + 3 = 9 \)
    - **Step 3**: \( i = 2 \): \( S = 9 + 1 + 2 + 3 = 15 \)

3. **End of Loop**: The loop runs for \( i \) values from 0 to 2 (since \( N - 1 = 3 \)). After the loop ends, the final value of \( S \) is 15.

Therefore, the completed table would look like this:

\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Step} & 0 & 1 & 2 & 3 \\
\hline
S & 0 & 4 & 9 & 15 \\
\hline
\end{array}
\]

### Do you want further details or have any questions?

Here are five related questions for further exploration:

1. How would the algorithm change if \( S \) started with a non-zero value?
2. What happens to the table if we change \( N \) to a different value, like \( N = 5 \)?
3. How can this algorithm be modified to subtract values instead of adding them?
4. What would be the impact of changing the range to \( range(0, N) \)?
5. How would the algorithm work if the loop incremented \( i \) by 2 instead of 1?

**Tip**: Understanding how a loop affects the variable values step by step is crucial in debugging and predicting the algorithm's behavior.

Complete the algorithm for N=4 and summarize the results obtained in each step in the table.

Learn how to execute an algorithm that calculates the summation of values using a loop. This problem involves understanding basic programming concepts and summation steps. Suitable for students in Grades 7-9.

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