6) Sum square difference

The sum of the squares of the first ten natural numbers is, 12 + 22 + ... + 102 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)2 = 552 = 3025 Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640. Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

by fosco

JavaScript

var n = 100,
    //Sums of the First n Natural Numbers
    sumOfNaturalNumbers = (n * (n + 1)) / 2,
    //Sum of the Squares of the First n Natural Numbers
    sumOfSquareRootNumbers = (n * (n + 1) * (2 * n + 1)) / 6,
    squareRootOfSumOfNaturalNumbers = Math.pow(sumOfNaturalNumbers, 2),
    difference = squareRootOfSumOfNaturalNumbers - sumOfSquareRootNumbers;

console.log(difference); //25164150