九连环是中国的一种古老智力游戏,它用九个圆环相连成串,环环相扣,以解开为胜,趣味无穷.中国的末代皇帝溥仪
也曾有一个精美的由九个翡翠缳相连的银制的九连环(如图).现假设有
个圆环,用
表示按照某种规则解下
个圆环所需的银和翠玉制九连环最少移动次数,且数列
满足
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb83a7551b340214df33f28095099ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
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21-22高三上·四川资阳·阶段练习 查看更多[5]
四川省资阳市2021-2022学年高三第一次诊断考试数学(文)试题宁夏石嘴山市平罗中学2022届高三上学期第三次月考数学(文)试题(已下线)热点01 数学传统文化和实际民生为载体的创新题-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)专题13 数列的性质必刷小题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)(已下线)第03讲 等比数列及其前n项和 (练)-2023年高考数学一轮复习讲练测(新教材新高考)
更新时间:2021-11-16 10:21:49
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【推荐2】数学家杨辉在其专著《详解九章算术法》和《算法通变本末》中,提出了一些新的高阶等差数列.其中二阶等差数列是一个常见的高阶等差数列,如数列2,4,7,11,16从第二项起,每一项与前一项的差组成的新数列2,3,4,5是等差数列,则称数列2,4,7,11,16为二阶等差数列.现有二阶等差数列
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【推荐1】在数列
中,
,
(
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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【推荐2】设等比数列
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_____ .
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【推荐1】宋元时期著名数学家朱世杰在其巨著《四元玉鉴》中利用“招差术”得到以下公式:
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[k·(k+1)(k+2)-(k-1)k(k+1)],
∴
k(k+1)=
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n(n+1)(n+2).
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∴
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【推荐2】著名的斐波那契数列
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