C Program to Evaluate the Series 1² + 2² + 3² + … + n²

Introduction

Summing squares of natural numbers is a classic example in mathematics and programming. This tutorial explains how to write a C program to evaluate the series 1² + 2² + 3² + … + n². This program uses loops and arithmetic operations to calculate the sum efficiently.

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Understanding the Series

The formula for the sum of squares from 1 to n is:

Sum = 1² + 2² + 3² + … + n² = n(n + 1)(2n + 1) / 6

But in this blog, we’ll compute it using a loop to practice iteration and accumulation.

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C Program to Evaluate the Series

#include <stdio.h>

int main() {
    int n, i, sum = 0;

    printf("Enter the value of n: ");
    scanf("%d", &n);

    for(i = 1; i <= n; i++) {
        sum += i * i;
    }

    printf("Sum of the series 1² + 2² + ... + %d² = %d\n", n, sum);

    return 0;
}

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Explanation of the Code

• Input: Accepts a positive integer n from the user.
• Logic: A loop runs from 1 to n, squaring each number and adding it to sum.
• Output: Displays the result of the accumulated sum of squares.

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Sample Output

Enter the value of n: 5  
Sum of the series 1² + 2² + ... + 5² = 55

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Real-World Applications

• Used in statistical calculations
• Physics-based simulations
• Performance analysis in algorithm loops
• Education and testing platforms

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Conclusion

This C program to evaluate square series helps learners understand loop operations and summation logic. You can try both the manual loop and the formula approach to compare accuracy and efficiency.