75 lines
2.8 KiB
Markdown
75 lines
2.8 KiB
Markdown
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---
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id: 5a23c84252665b21eecc8041
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title: Sum of a series
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challengeType: 5
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---
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## Description
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<section id='description'>
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Compute the <b>n</b><sup>th</sup> term of a <a href="https://en.wikipedia.org/wiki/Series (mathematics)">series</a>, i.e. the sum of the <b>n</b> first terms of the corresponding <a href="https://en.wikipedia.org/wiki/sequence">sequence</a>.
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Informally this value, or its limit when <b>n</b> tends to infinity, is also called the <i>sum of the series</i>, thus the title of this task.
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For this task, use:
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$S_n = \sum_{k=1}^n \frac{1}{k^2}$
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and compute $S_{1000}$
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This approximates the <a href="https://en.wikipedia.org/wiki/Riemann zeta function">zeta function</a> for S=2, whose exact value
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$\zeta(2) = {\pi^2\over 6}$
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is the solution of the <a href="https://en.wikipedia.org/wiki/Basel problem">Basel problem</a>.
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Write a function that take $a$ and $b$ as parameters and returns the sum of $a^{th}$ to $b^{th}$ members of the sequence.
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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>sum</code> should be a function.
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testString: assert(typeof sum == 'function', '<code>sum</code> should be a function.');
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- text: <code>sum(1, 100)</code> should return a number.
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testString: assert(typeof sum(1, 100) == 'number', '<code>sum(1, 100)</code> should return a number.');
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- text: <code>sum(1, 100)</code> should return <code>1.6349839001848923</code>.
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testString: assert.equal(sum(1, 100), 1.6349839001848923, '<code>sum(1, 100)</code> should return <code>1.6349839001848923</code>.');
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- text: <code>sum(33, 46)</code> should return <code>0.009262256361481223</code>.
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testString: assert.equal(sum(33, 46), 0.009262256361481223, '<code>sum(33, 46)</code> should return <code>0.009262256361481223</code>.');
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- text: <code>sum(21, 213)</code> should return <code>0.044086990748706555</code>.
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testString: assert.equal(sum(21, 213), 0.044086990748706555, '<code>sum(21, 213)</code> should return <code>0.044086990748706555</code>.');
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- text: <code>sum(11, 111)</code> should return <code>0.08619778593108679</code>.
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testString: assert.equal(sum(11, 111), 0.08619778593108679, '<code>sum(11, 111)</code> should return <code>0.08619778593108679</code>.');
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- text: <code>sum(1, 10)</code> should return <code>1.5497677311665408</code>.
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testString: assert.equal(sum(1, 10), 1.5497677311665408, '<code>sum(1, 10)</code> should return <code>1.5497677311665408</code>.');
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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 sum (a, b) {
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// Good luck!
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}
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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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function sum (a, b) {
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function fn(x) {
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return 1 / (x * x)
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}
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var s = 0;
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for (; a <= b; a++) s += fn(a);
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return s;
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}
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```
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</section>
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