80 lines
2.0 KiB
Markdown
80 lines
2.0 KiB
Markdown
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---
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id: 5
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localeTitle: 5900f3721000cf542c50fe85
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challengeType: 5
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title: 'Problem 6: Sum square difference'
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---
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## Description
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<section id='description'>
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La suma de los cuadrados de los primeros diez números naturales es,
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<div style='text-align: center;'> 1 <sup>2</sup> + 2 <sup>2</sup> + ... + 10 <sup>2</sup> = 385 </div>
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El cuadrado de la suma de los primeros diez números naturales es,
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<div style='text-align: center;'> (1 + 2 + ... + 10) <sup>2</sup> = 55 <sup>2</sup> = 3025 </div>
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Por lo tanto, la diferencia entre la suma de los cuadrados de los primeros diez números naturales y el cuadrado de la suma es 3025 - 385 = 2640.
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Halla la diferencia entre la suma de los cuadrados de los primeros <code>n</code> números naturales y el cuadrado de suma.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>sumSquareDifference(10)</code> debe devolver 2640.
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testString: 'assert.strictEqual(sumSquareDifference(10), 2640, "<code>sumSquareDifference(10)</code> should return 2640.");'
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- text: <code>sumSquareDifference(20)</code> debe devolver 41230.
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testString: 'assert.strictEqual(sumSquareDifference(20), 41230, "<code>sumSquareDifference(20)</code> should return 41230.");'
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- text: <code>sumSquareDifference(100)</code> debe devolver 25164150.
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testString: 'assert.strictEqual(sumSquareDifference(100), 25164150, "<code>sumSquareDifference(100)</code> should return 25164150.");'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function sumSquareDifference(n) {
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// Good luck!
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return true;
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}
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sumSquareDifference(100);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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const sumSquareDifference = (number)=>{
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let squareOfSum = Math.pow(sumOfArithmeticSeries(1,1,number),2);
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let sumOfSquare = sumOfSquareOfNumbers(number);
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return squareOfSum - sumOfSquare;
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}
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function sumOfArithmeticSeries(a,d,n){
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return (n/2)*(2*a+(n-1)*d);
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}
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function sumOfSquareOfNumbers(n){
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return (n*(n+1)*(2*n+1))/6;
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}
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```
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</section>
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