2018-10-10 22:03:03 +00:00
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id: 5900f3a51000cf542c50feb8
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2020-12-16 07:37:30 +00:00
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title: 问题57：平方根收敛
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2018-10-10 22:03:03 +00:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 02:31:00 +00:00
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dashedName: problem-57-square-root-convergents
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2018-10-10 22:03:03 +00:00
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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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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？
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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# --hints--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`euler57()`应返回153。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(euler57(), 153);
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2018-10-10 22:03:03 +00:00
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```
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2021-01-13 02:31:00 +00:00
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# --seed--
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## --seed-contents--
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```js
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function squareRootConvergents() {
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return true;
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}
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squareRootConvergents();
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```
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2020-12-16 07:37:30 +00:00
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# --solutions--
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2020-08-13 15:24:35 +00:00
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2021-01-13 02:31:00 +00:00
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```js
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// solution required
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```
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