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Problem 6: Sum square difference

curriculum/challenges/english/blocks/project-euler-problems-1-to-100/5900f3721000cf542c50fe85.md

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--description--

The sum of the squares of the first ten natural numbers is,

<div style='text-align: center;'>1<sup>2</sup> + 2<sup>2</sup> + ... + 10<sup>2</sup> = 385</div>

The square of the sum of the first ten natural numbers is,

<div style='text-align: center;'>(1 + 2 + ... + 10)<sup>2</sup> = 55<sup>2</sup> = 3025</div>

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 n natural numbers and the square of the sum.

--hints--

sumSquareDifference(10) should return a number.

js
assert.isNumber(sumSquareDifference(10));

sumSquareDifference(10) should return 2640.

js
assert.strictEqual(sumSquareDifference(10), 2640);

sumSquareDifference(20) should return 41230.

js
assert.strictEqual(sumSquareDifference(20), 41230);

sumSquareDifference(100) should return 25164150.

js
assert.strictEqual(sumSquareDifference(100), 25164150);

--seed--

--seed-contents--

js
function sumSquareDifference(n) {

  return true;
}

sumSquareDifference(100);

--solutions--

js
const sumSquareDifference = (number)=>{
  let squareOfSum = Math.pow(sumOfArithmeticSeries(1,1,number),2);
  let sumOfSquare = sumOfSquareOfNumbers(number);
 return squareOfSum - sumOfSquare;
}

function sumOfArithmeticSeries(a,d,n){
  return (n/2)*(2*a+(n-1)*d);
}

function sumOfSquareOfNumbers(n){
 return (n*(n+1)*(2*n+1))/6;
}