fix: replace .english.md extension with .md

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-65-convergents-of-e.md

@@ -0,0 +1,84 @@
+---
+id: 5900f3ad1000cf542c50fec0
+challengeType: 5
+title: 'Problem 65: Convergents of e'
+forumTopicId: 302177
+---
+
+## Description
+<section id='description'>
+
+The square root of 2 can be written as an infinite continued fraction.
+
+$\sqrt{2} = 1 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ...}}}}$
+
+The infinite continued fraction can be written, $\sqrt{2} = [1; (2)]$ indicates that 2 repeats <i>ad infinitum</i>. In a similar way, $\sqrt{23} = [4; (1, 3, 1, 8)]$.
+It turns out that the sequence of partial values of continued fractions for square roots provide the best rational approximations. Let us consider the convergents for $\sqrt{2}$.
+
+$1 + \dfrac{1}{2} = \dfrac{3}{2}\\\\
+1 + \dfrac{1}{2 + \dfrac{1}{2}} = \dfrac{7}{5}\\\\
+1 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2}}} = \dfrac{17}{12}\\\\
+1 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2}}}} = \dfrac{41}{29}$
+
+Hence the sequence of the first ten convergents for $\sqrt{2}$ are:
+
+$1, \dfrac{3}{2}, \dfrac{7}{5}, \dfrac{17}{12}, \dfrac{41}{29}, \dfrac{99}{70}, \dfrac{239}{169}, \dfrac{577}{408}, \dfrac{1393}{985}, \dfrac{3363}{2378}, ...$
+
+What is most surprising is that the important mathematical constant, $e = [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, ... , 1, 2k, 1, ...]$.
+The first ten terms in the sequence of convergents for <var>e</var> are:
+
+$2, 3, \dfrac{8}{3}, \dfrac{11}{4}, \dfrac{19}{7}, \dfrac{87}{32}, \dfrac{106}{39}, \dfrac{193}{71}, \dfrac{1264}{465}, \dfrac{1457}{536}, ...$
+
+The sum of digits in the numerator of the 10<sup>th</sup> convergent is $1 + 4 + 5 + 7 = 17$.
+
+Find the sum of digits in the numerator of the 100<sup>th</sup> convergent of the continued fraction for <var>e</var>.
+
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>convergentsOfE()</code> should return a number.
+    testString: assert(typeof convergentsOfE() === 'number');
+  - text: <code>convergentsOfE()</code> should return 272.
+    testString: assert.strictEqual(convergentsOfE(), 272);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function convergentsOfE() {
+
+  return true;
+}
+
+convergentsOfE();
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+```js
+// solution required
+```
+
+</section>