freeCodeCamp/curriculum/challenges/chinese/10-coding-interview-prep/rosetta-code/sum-of-a-series.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc8041	Sum of a series	5	302333	sum-of-a-series

--description--

Compute the n^th term of a series, i.e. the sum of the n first terms of the corresponding 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).

--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.

assert(typeof sum == 'function');

sum(1, 100) should return a number.

assert(typeof sum(1, 100) == 'number');

sum(1, 100) should return 1.6349839001848923.

assert.equal(sum(1, 100), 1.6349839001848923);

sum(33, 46) should return 0.009262256361481223.

assert.equal(sum(33, 46), 0.009262256361481223);

sum(21, 213) should return 0.044086990748706555.

assert.equal(sum(21, 213), 0.044086990748706555);

sum(11, 111) should return 0.08619778593108679.

assert.equal(sum(11, 111), 0.08619778593108679);

sum(1, 10) should return 1.5497677311665408.

assert.equal(sum(1, 10), 1.5497677311665408);

--seed--

--seed-contents--

function sum(a, b) {

}

--solutions--

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