56 lines
1.3 KiB
Markdown
56 lines
1.3 KiB
Markdown
---
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id: 5900f3a51000cf542c50feb8
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challengeType: 5
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title: 'Problem 57: Square root convergents'
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videoUrl: ''
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localeTitle: 问题57：平方根收敛
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---
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## Description
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<section id="description">可以证明两个的平方根可以表示为无限连续分数。 √2= 1 + 1 /（2 + 1 /（2 + 1 /（2 + ...）））= 1.414213 ...通过扩展前四次迭代，得到：1 + 1/2 = 3 / 2 = 1.5 1 + 1 /（2 + 1/2）= 7/5 = 1.4 1 + 1 /（2 + 1 /（2 + 1/2））= 17/12 = 1.41666 ... 1 + 1 /（2 + 1 /（2 + 1 /（2 + 1/2）））= 41/29 = 1.41379 ...接下来的三次扩展是99 / 70,239 / 169和577/408，但是第八次扩展，1393/985，是分子中位数超过分母中位数的第一个例子。在前一千次扩展中，有多少分数包含一个数字比分母更多的分子？ </section>
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## Instructions
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<section id="instructions">
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler57()</code>应返回153。
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testString: 'assert.strictEqual(euler57(), 153, "<code>euler57()</code> should return 153.");'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler57() {
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// Good luck!
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return true;
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}
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euler57();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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