2020-12-16 07:37:30 +00:00
---
id: 5a23c84252665b21eecc8041
title: Sum of a series
challengeType: 5
forumTopicId: 302333
2021-01-13 02:31:00 +00:00
dashedName: sum-of-a-series
2020-12-16 07:37:30 +00:00
---
# --description--
2021-07-15 07:34:11 +00:00
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: $S_n = \displaystyle\sum_{k=1}^n \frac{1}{k^2}$.
2020-12-16 07:37:30 +00:00
# --instructions--
Write a function that take $a$ and $b$ as parameters and returns the sum of $a^{th}$ to $b^{th}$ members of the sequence.
# --hints--
`sum` should be a function.
```js
assert(typeof sum == 'function');
```
`sum(1, 100)` should return a number.
```js
assert(typeof sum(1, 100) == 'number');
```
`sum(1, 100)` should return `1.6349839001848923` .
```js
assert.equal(sum(1, 100), 1.6349839001848923);
```
`sum(33, 46)` should return `0.009262256361481223` .
```js
assert.equal(sum(33, 46), 0.009262256361481223);
```
`sum(21, 213)` should return `0.044086990748706555` .
```js
assert.equal(sum(21, 213), 0.044086990748706555);
```
`sum(11, 111)` should return `0.08619778593108679` .
```js
assert.equal(sum(11, 111), 0.08619778593108679);
```
`sum(1, 10)` should return `1.5497677311665408` .
```js
assert.equal(sum(1, 10), 1.5497677311665408);
```
# --seed--
## --seed-contents--
```js
function sum(a, b) {
}
```
# --solutions--
```js
function sum(a, b) {
function fn(x) {
return 1 / (x * x);
}
var s = 0;
for (; a < = b; a++) s += fn(a);
return s;
}
```