C Program To Print Integer Sum Of Numbers Upto 100 Natural

Calculating the sum of a sequence of numbers is a fundamental operation in programming and mathematics. Whether you're analyzing data, performing financial calculations, or simply learning basic programming concepts, understanding how to sum a series of numbers is a valuable skill.

In this article, you will learn how to write C programs to calculate the sum of natural numbers up to 100 using various approaches, including iterative methods and a direct mathematical formula.

Problem Statement

The goal is to find the sum of all natural numbers from 1 to 100. Natural numbers are positive integers (1, 2, 3, ...). Mathematically, this can be represented as 1 + 2 + 3 + ... + 99 + 100. This kind of summation is common in various computational tasks where you need to aggregate sequential data.

Example

The desired output for the sum of natural numbers up to 100 will be:

The sum of natural numbers up to 100 is: 5050

Background & Knowledge Prerequisites

To understand the solutions presented in this article, you should have a basic understanding of:

• C Programming Basics: How to compile and run a simple C program.
• Variables: Declaring and using integer variables (int).
• Arithmetic Operations: Basic operations like addition (+) and assignment (=).
• Loops: Concepts of for loops and while loops for iteration.
• printf() Function: For displaying output to the console.

Use Cases or Case Studies

Summing a series of numbers has practical applications across many domains:

• Financial Calculations: Calculating compound interest over periods or summing up monthly expenses.
• Statistical Analysis: Finding the sum of a dataset before calculating averages or standard deviations.
• Algorithmic Foundations: Many algorithms rely on iterative summation, such as calculating series for approximations (e.g., Taylor series).
• Game Development: Tracking scores, resource accumulation, or sequential event counts.
• Data Aggregation: Simple report generation where you need total counts or sums of numerical attributes.

Solution Approaches

Here are three common approaches to sum natural numbers up to 100 in C.

Approach 1: Using a for Loop (Iterative Method)

This approach uses a for loop to iterate from 1 to 100, adding each number to a running total.

One-line summary

Iterate from 1 to 100 using a for loop, accumulating the sum in each step.

Code example

// Sum of Natural Numbers up to 100 (for loop)
#include <stdio.h>

int main() {
    // Step 1: Declare variables for sum and counter
    int sum = 0;
    int i;

    // Step 2: Use a for loop to iterate from 1 to 100
    for (i = 1; i <= 100; i++) {
        // Step 3: Add the current number to the sum
        sum += i; // This is equivalent to sum = sum + i;
    }

    // Step 4: Print the final sum
    printf("The sum of natural numbers up to 100 is: %d\\n", sum);

    return 0;
}

Run

Sample output

The sum of natural numbers up to 100 is: 5050

Stepwise explanation

1. Initialization: An integer variable sum is initialized to 0. This variable will store the accumulating sum. An integer i is declared as the loop counter.
2. for Loop: The loop starts with i = 1.
3. Condition: The loop continues as long as i is less than or equal to 100.
4. Iteration: In each iteration, the current value of i is added to sum (sum += i).
5. Increment: After each iteration, i is incremented by 1 (i++).
6. Output: Once the loop finishes (when i becomes 101), the final value of sum is printed.

Approach 2: Using a while Loop (Iterative Method)

Similar to the for loop, a while loop can also be used to achieve the same result by manually handling initialization, condition, and increment.

One-line summary

Initialize a counter and sum, then use a while loop to add numbers from 1 to 100 until the counter exceeds 100.

Code example

// Sum of Natural Numbers up to 100 (while loop)
#include <stdio.h>

int main() {
    // Step 1: Declare and initialize variables
    int sum = 0;
    int i = 1; // Starting counter from 1

    // Step 2: Use a while loop to iterate
    while (i <= 100) {
        // Step 3: Add the current number to the sum
        sum += i;

        // Step 4: Increment the counter
        i++;
    }

    // Step 5: Print the final sum
    printf("The sum of natural numbers up to 100 is: %d\\n", sum);

    return 0;
}

Run

Sample output

The sum of natural numbers up to 100 is: 5050

Stepwise explanation

1. Initialization: sum is set to 0, and the loop counter i is set to 1.
2. while Loop: The loop continues as long as the condition i <= 100 is true.
3. Addition: Inside the loop, i is added to sum.
4. Increment: The counter i is explicitly incremented by 1 in each iteration. Without this, the loop would run indefinitely.
5. Output: After i exceeds 100, the loop terminates, and the final sum is displayed.

Approach 3: Using a Mathematical Formula (Direct Method)

For summing consecutive natural numbers, there's a well-known mathematical formula: n * (n + 1) / 2, where n is the last number in the sequence. This method is highly efficient, especially for large n.

One-line summary

Apply the mathematical formula n * (n + 1) / 2 to directly calculate the sum without iteration.

Code example

// Sum of Natural Numbers up to 100 (Formula)
#include <stdio.h>

int main() {
    // Step 1: Define the upper limit (n)
    int n = 100;

    // Step 2: Calculate the sum using the formula
    int sum = n * (n + 1) / 2;

    // Step 3: Print the final sum
    printf("The sum of natural numbers up to 100 is: %d\\n", sum);

    return 0;
}

Run

Sample output

The sum of natural numbers up to 100 is: 5050

Stepwise explanation

1. Define n: An integer variable n is set to 100, representing the upper limit of the natural numbers to sum.
2. Calculate Sum: The formula n * (n + 1) / 2 is directly applied to n to compute the sum. For n = 100, this becomes 100 * (100 + 1) / 2 = 100 * 101 / 2 = 10100 / 2 = 5050.
3. Output: The calculated sum is then printed. This method is much faster than iterative methods for very large n because it performs a fixed number of operations regardless of n.

Conclusion

You have explored three distinct ways to calculate the sum of natural numbers up to 100 in C programming. The iterative approaches using for and while loops demonstrate fundamental programming constructs and are excellent for understanding how to accumulate values over a sequence. The direct mathematical formula offers a highly efficient, non-iterative solution, showcasing the power of mathematical insights in programming. Each method has its advantages depending on the specific problem context and performance requirements.

Summary

• Problem: Sum natural numbers from 1 to 100.
• for Loop: Iterates from 1 to 100, adding each number to a sum variable.
• while Loop: Similar to for, but explicitly manages the loop counter's initialization, condition, and increment.
• Mathematical Formula: Uses n * (n + 1) / 2 for a direct, highly efficient calculation, especially for large n.
• Result: All methods correctly yield 5050.