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

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+---
+id: 5a23c84252665b21eecc8041
+title: Sum of a series
+challengeType: 5
+forumTopicId: 302333
+dashedName: sum-of-a-series
+---
+
+# --description--
+
+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: $S_n = \displaystyle\sum_{k=1}^n \frac{1}{k^2}$.
+
+# --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;
+}
+```