freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/sum-of-a-series.md

id	title	challengeType
5a23c84252665b21eecc8041	Sum of a series	5

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 for S=2, whose exact value $\zeta(2) = {\pi^2\over 6}$ is the solution of the Basel problem. Write a function that take $a$ and $b$ as parameters and returns the sum of $a^{th}$ to $b^{th}$ members of the sequence.

Instructions

Tests

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>.');

Challenge Seed

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

Solution

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