---
id: 5a23c84252665b21eecc8041
title: Sum of a series
challengeType: 5
---

## Description
<section id='description'>
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>.
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.
For this task, use:
$S_n = \sum_{k=1}^n \frac{1}{k^2}$
and compute  $S_{1000}$
This approximates the   <a href="https://en.wikipedia.org/wiki/Riemann zeta function">zeta function</a>  for  S=2,  whose exact value
$\zeta(2) = {\pi^2\over 6}$
is the solution of the <a href="https://en.wikipedia.org/wiki/Basel problem">Basel problem</a>.
Write a function that take $a$ and $b$ as parameters and returns the sum of $a^{th}$ to $b^{th}$ members of the sequence.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

``` yml
tests:
  - text: <code>sum</code> should be a function.
    testString: assert(typeof sum == 'function', '<code>sum</code> should be a function.');
  - text: <code>sum(1, 100)</code> should return a number.
    testString: assert(typeof sum(1, 100) == 'number', '<code>sum(1, 100)</code> should return a number.');
  - text: <code>sum(1, 100)</code> should return <code>1.6349839001848923</code>.
    testString: assert.equal(sum(1, 100), 1.6349839001848923, '<code>sum(1, 100)</code> should return <code>1.6349839001848923</code>.');
  - text: <code>sum(33, 46)</code> should return <code>0.009262256361481223</code>.
    testString: assert.equal(sum(33, 46), 0.009262256361481223, '<code>sum(33, 46)</code> should return <code>0.009262256361481223</code>.');
  - text: <code>sum(21, 213)</code> should return <code>0.044086990748706555</code>.
    testString: assert.equal(sum(21, 213), 0.044086990748706555, '<code>sum(21, 213)</code> should return <code>0.044086990748706555</code>.');
  - text: <code>sum(11, 111)</code> should return <code>0.08619778593108679</code>.
    testString: assert.equal(sum(11, 111), 0.08619778593108679, '<code>sum(11, 111)</code> should return <code>0.08619778593108679</code>.');
  - text: <code>sum(1, 10)</code> should return <code>1.5497677311665408</code>.
    testString: assert.equal(sum(1, 10), 1.5497677311665408, '<code>sum(1, 10)</code> should return <code>1.5497677311665408</code>.');
```

</section>

## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>

```js
function sum (a, b) {
  // Good luck!
}
```

</div>
</section>

## Solution
<section id='solution'>

```js
function sum (a, b) {
  function fn(x) {
    return 1 / (x * x)
  }
  var s = 0;
  for (; a <= b; a++) s += fn(a);
  return s;
}
```

</section>