Sum of N Numbers in C++

 

Calculating the sum of the first N numbers is a common task. You can approach this using various types of loops, such as for, while, or do-while loops. Below are a few examples to help you understand how to implement this.

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1️⃣ Example: Using for Loop to Sum N Numbers

In this example, we calculate the sum of the first N natural numbers (1, 2, 3, ..., N) using a for loop:

#include <iostream>
using namespace std;

int main() {
    int N, sum = 0;

    // Taking input from the user
    cout << "Enter a positive integer: ";
    cin >> N;

    // for loop to calculate the sum
    for (int i = 1; i <= N; i++) {
        sum += i;  // Add i to sum
    }

    cout << "The sum of the first " << N << " numbers is: " << sum << endl;

    return 0;
}

Explanation:

• The user inputs a positive integer N.
• The for loop runs from 1 to N, and in each iteration, it adds the current value of i to the sum.
• Finally, the sum is printed.

Output (Example when N = 5):

Enter a positive integer: 5
The sum of the first 5 numbers is: 15

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2️⃣ Example: Using while Loop to Sum N Numbers

Here’s an implementation using a while loop to calculate the sum of the first N numbers:

#include <iostream>
using namespace std;

int main() {
    int N, sum = 0, i = 1;

    // Taking input from the user
    cout << "Enter a positive integer: ";
    cin >> N;

    // while loop to calculate the sum
    while (i <= N) {
        sum += i;  // Add i to sum
        i++;       // Increment i
    }

    cout << "The sum of the first " << N << " numbers is: " << sum << endl;

    return 0;
}

Explanation:

• The loop runs as long as i <= N, and in each iteration, i is added to sum.
• After each iteration, i is incremented.

Output (Example when N = 5):

Enter a positive integer: 5
The sum of the first 5 numbers is: 15

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3️⃣ Example: Using do-while Loop to Sum N Numbers

You can also use a do-while loop to calculate the sum. Here’s how:

#include <iostream>
using namespace std;

int main() {
    int N, sum = 0, i = 1;

    // Taking input from the user
    cout << "Enter a positive integer: ";
    cin >> N;

    // do-while loop to calculate the sum
    do {
        sum += i;  // Add i to sum
        i++;       // Increment i
    } while (i <= N);

    cout << "The sum of the first " << N << " numbers is: " << sum << endl;

    return 0;
}

Explanation:

• The loop will always execute at least once, as it checks the condition after the first iteration.
• Similar to the previous examples, i is added to sum in each iteration.

Output (Example when N = 5):

Enter a positive integer: 5
The sum of the first 5 numbers is: 15

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4️⃣ Formula to Calculate the Sum of First N Numbers

You can also use the mathematical formula to calculate the sum of the first N natural numbers instead of looping:

Formula:

$$\text{Sum} = \frac{N \times (N + 1)}{2}$$

This formula works because the sum of the first N numbers is a series of consecutive numbers starting from 1. The sum of such a series is given by the formula.

Here’s an example using this formula:

#include <iostream>
using namespace std;

int main() {
    int N;

    // Taking input from the user
    cout << "Enter a positive integer: ";
    cin >> N;

    // Using the formula to calculate the sum
    int sum = (N * (N + 1)) / 2;

    cout << "The sum of the first " << N << " numbers is: " << sum << endl;

    return 0;
}

Explanation:

• The sum is calculated directly using the formula without using a loop.

Output (Example when N = 5):

Enter a positive integer: 5
The sum of the first 5 numbers is: 15

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5️⃣ Key Points to Remember:

• The for, while, and do-while loops are useful for iterating and performing repetitive tasks like summing numbers.
• The formula method is more efficient because it doesn't require looping and directly computes the result in constant time.
• Ensure you handle user input and edge cases like invalid or zero input if necessary.

Would you like more examples or details on using loops for other tasks, such as multiplication tables or factorial calculations?