Math Problem Statement

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

Solution

The image presents an algorithm in Python, followed by an instruction to execute it for N=4N = 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=4N = 4, we can analyze and determine the values for each step:

  1. Initial Setup: S=0S = 0, N=4N = 4.

  2. Loop Execution:

    • Step 1: i=0i = 0: S=0+1+0+3=4S = 0 + 1 + 0 + 3 = 4
    • Step 2: i=1i = 1: S=4+1+1+3=9S = 4 + 1 + 1 + 3 = 9
    • Step 3: i=2i = 2: S=9+1+2+3=15S = 9 + 1 + 2 + 3 = 15
  3. End of Loop: The loop runs for ii values from 0 to 2 (since N1=3N - 1 = 3). After the loop ends, the final value of SS is 15.

Therefore, the completed table would look like this:

\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.

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Math Problem Analysis

Mathematical Concepts

Programming
Summation

Formulas

S = S + 1 + i + 3

Theorems

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Suitable Grade Level

Grades 7-9