6cfd0fc503
* fix: improve Project Euler descriptions and test case Improve formatting of Project Euler test descriptions. Also add poker hands array and new test case for problem 54 * feat: add typeof tests and gave functions proper names for first 100 challenges * fix: continue fixing test descriptions and adding "before test" sections * fix: address review comments * fix: adjust grids in 18 and 67 and fix some text that reference files rather than the given arrays * fix: implement bug fixes and improvements from review * fix: remove console.log statements from seed and solution
1.7 KiB
1.7 KiB
id, challengeType, title, forumTopicId
| id | challengeType | title | forumTopicId |
|---|---|---|---|
| 5900f3a51000cf542c50feb8 | 5 | Problem 57: Square root convergents | 302168 |
Description
It is possible to show that the square root of two can be expressed as an infinite continued fraction.
$\sqrt 2 =1+ \frac 1 {2+ \frac 1 {2 +\frac 1 {2+ \dots}}}$
By expanding this for the first four iterations, we get:
1 + \frac 1 2 = \frac 32 = 1.5
1 + \frac 1 {2 + \frac 1 2} = \frac 7 5 = 1.4
1 + \frac 1 {2 + \frac 1 {2+\frac 1 2}} = \frac {17}{12} = 1.41666 \dots
1 + \frac 1 {2 + \frac 1 {2+\frac 1 {2+\frac 1 2}}} = \frac {41}{29} = 1.41379 \dots
The next three expansions are \frac {99}{70}, \frac {239}{169}, and \frac {577}{408}, but the eighth expansion, \frac {1393}{985}, is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.
In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?
Instructions
Tests
tests:
- text: <code>squareRootConvergents()</code> should return a number.
testString: assert(typeof squareRootConvergents() === 'number');
- text: <code>squareRootConvergents()</code> should return 153.
testString: assert.strictEqual(squareRootConvergents(), 153);
Challenge Seed
function squareRootConvergents() {
// Good luck!
return true;
}
squareRootConvergents();
Solution
// solution required