PHP program to calculate the sum of square of first n natural numbers

To calculate the sum of square of first n natural numbers in PHP, we can use a simple loop to iterate through each number and add its square to the running total.

Example

Here's a PHP function that calculates the sum of squares ?

<?php
function sum_of_squares($limit)
{
    $ini_sum = 0;
    for ($i = 1; $i <= $limit; $i++)
        $ini_sum += ($i * $i);
    return $ini_sum;
}
$limit = 5;
print_r("The sum of square of first 5 natural numbers is ");
echo sum_of_squares($limit);
?>

Output

The sum of square of first 5 natural numbers is 55

How It Works

A function named sum_of_squares is defined that takes the limit up to which square of natural numbers needs to be found. In this function, a sum value is initialized to 0. A for loop runs from 1 to the limit value. In each iteration, the square of the current number ($i * $i) is added to the sum variable. When the loop completes, the function returns the total sum.

Mathematical Formula

The sum of squares of first n natural numbers can also be calculated using the formula: n(n+1)(2n+1)/6. Here's an alternative implementation ?

<?php
function sum_of_squares_formula($n)
{
    return ($n * ($n + 1) * (2 * $n + 1)) / 6;
}
$limit = 5;
echo "Using formula: " . sum_of_squares_formula($limit);
?>

Using formula: 55

Conclusion

Both approaches give the same result. The loop method is easier to understand, while the mathematical formula is more efficient for large values of n.