83 lines
1.9 KiB
Markdown
83 lines
1.9 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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forumTopicId: 302333
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dashedName: sum-of-a-series
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---
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# --description--
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Compute the **n**<sup>th</sup> term of a [series](https://en.wikipedia.org/wiki/Series (mathematics)), i.e. the sum of the **n** first terms of the corresponding [sequence](https://en.wikipedia.org/wiki/sequence). Informally this value, or its limit when **n** tends to infinity, is also called the *sum of the series*, thus the title of this task. For this task, use: $S*n = \\sum*{k=1}^n \\frac{1}{k^2}$ and compute $S\_{1000}$ This approximates the [zeta function](https://en.wikipedia.org/wiki/Riemann zeta function) for S=2, whose exact value $\\zeta(2) = {\\pi^2\\over 6}$ is the solution of the [Basel problem](https://en.wikipedia.org/wiki/Basel problem).
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# --instructions--
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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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# --hints--
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`sum` should be a function.
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```js
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assert(typeof sum == 'function');
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```
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`sum(1, 100)` should return a number.
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```js
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assert(typeof sum(1, 100) == 'number');
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```
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`sum(1, 100)` should return `1.6349839001848923`.
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```js
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assert.equal(sum(1, 100), 1.6349839001848923);
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```
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`sum(33, 46)` should return `0.009262256361481223`.
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```js
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assert.equal(sum(33, 46), 0.009262256361481223);
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```
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`sum(21, 213)` should return `0.044086990748706555`.
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```js
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assert.equal(sum(21, 213), 0.044086990748706555);
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```
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`sum(11, 111)` should return `0.08619778593108679`.
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```js
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assert.equal(sum(11, 111), 0.08619778593108679);
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```
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`sum(1, 10)` should return `1.5497677311665408`.
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```js
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assert.equal(sum(1, 10), 1.5497677311665408);
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```
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# --seed--
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## --seed-contents--
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```js
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function sum(a, b) {
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}
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```
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# --solutions--
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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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