Sum of squares of first n natural numbers in C Program?

In C programming, finding the sum of squares of the first n natural numbers means calculating 1² + 2² + 3² + ... + n². This is a common mathematical problem that can be solved using different approaches.

Example: For n = 5, the sum is 1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55

Syntax

// Using loops
for(int i = 1; i <= n; i++) {
    sum += i * i;
}

// Using formula
sum = n * (n + 1) * (2 * n + 1) / 6;

Method 1: Using For Loop

This approach iterates through numbers from 1 to n, squares each number, and adds it to the sum −

#include <stdio.h>

int main() {
    int n = 5;
    int sum = 0;
    
    for (int i = 1; i <= n; i++) {
        sum += (i * i);
    }
    
    printf("The sum of squares of first %d natural numbers is %d<br>", n, sum);
    return 0;
}

The sum of squares of first 5 natural numbers is 55

Method 2: Using Mathematical Formula

The mathematical formula n(n+1)(2n+1)/6 provides a direct calculation without loops, making it more efficient −

#include <stdio.h>

int main() {
    int n = 10;
    int sum = (n * (n + 1) * (2 * n + 1)) / 6;
    
    printf("The sum of squares of first %d natural numbers is %d<br>", n, sum);
    return 0;
}

The sum of squares of first 10 natural numbers is 385

Comparison

Conclusion

Both methods solve the problem effectively, but the formula approach is preferred for larger values of n due to its constant time complexity. The loop method helps understand the underlying mathematical concept better.