* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
1017 B
1017 B
id, title, challengeType, videoUrl, dashedName
id | title | challengeType | videoUrl | dashedName |
---|---|---|---|---|
5900f3a51000cf542c50feb8 | 问题57:平方根收敛 | 5 | problem-57-square-root-convergents |
--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?
--hints--
euler57()
应返回153。
assert.strictEqual(euler57(), 153);
--seed--
--seed-contents--
function squareRootConvergents() {
return true;
}
squareRootConvergents();
--solutions--
// solution required