1 . “太极生两仪,两仪生四象,四象生八卦……”,“大衍数列”来源于《乾坤谱》,用于解释中国传统文化中的太极衍生原理.“大衍数列”
的前几项分别是:0,2,4,8,12,18,24,…,且
满足
其中
.
(1)求
(用
表示);
(2)设数列
满足:
其中
,
是
的前
项的积,求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd3170103ca714ed00d94d2427b420c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7f2a789507501bf6a96d3cb21cd35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ea9c623c95626b167ec21362607ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
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2023-11-11更新
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4卷引用:福建省莆田市第二中学2023-2024学年高二下学期返校考试数学试卷
福建省莆田市第二中学2023-2024学年高二下学期返校考试数学试卷江苏省盐城市2023-2024学年高三上学期期中数学试题重庆市2024届高三上学期11月月度质量检测数学试题(已下线)专题10 数列不等式的放缩问题 (7大核心考点)(讲义)
名校
解题方法
2 . 勒洛四面体是一个非常神奇的“四面体”,它能在两个平行平面间自由转动,并且始终保持与两平面都接触,因此它能像球一样来回滚动(如图甲),利用这一原理,科技人员发明了转子发动机.勒洛四面体是以正四面体的四个顶点为球心,以正四面体的棱长为半径的四个球的相交部分围成的几何体如图乙所示,若正四面体
的棱长为2,则下列说法正确的是___________ .
①勒洛四面体
被平面
截得的截面面积是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adde06771edb8cf91eb2b155d22ab13.png)
②勒洛四面体
内切球的半径是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c53416d8f74283ca656cd82ff25b68.png)
③勒洛四面体的截面面积的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda15c8e92bb4d6e455c9efc89ca4118.png)
④勒洛四面体能够容纳的最大球的半径为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4082e5635dcd90b7c61ce789aea2c427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①勒洛四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adde06771edb8cf91eb2b155d22ab13.png)
②勒洛四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c53416d8f74283ca656cd82ff25b68.png)
③勒洛四面体的截面面积的最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda15c8e92bb4d6e455c9efc89ca4118.png)
④勒洛四面体能够容纳的最大球的半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4082e5635dcd90b7c61ce789aea2c427.png)
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4卷引用:福建省泉州第一中学2022-2023学年高二上学期暑假返校数学试题
3 . 历史上数列的发展,折射出许多有价值的数学思想方法,对时代的进步起了重要的作用,比如意大利数学家列昂纳多·斐波那契以兔子繁殖为例,引入“兔子数列”:即1,1,2,3,5,8,13,21,34,55,89,144,233,….即
,
,此数列在现代物理、准晶体结构及化学等领域有着广泛的应用,若此数列被4整除后的余数构成一个新的数列
,又记数列
满足
,
,
,则
的值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b3fe135e3851c0f47aa35fab6c3df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbfe1cf9cba1825868a98774353181a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ea9e0ead7a42e1bcbe7d37d1a60954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df16fe634612dca8c2190784253971e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12882d20de941fb04c9e40db5b2223b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ac51b38479f181f9146dc54f598044.png)
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2019-04-24更新
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2卷引用:福建省福州市平潭翰英中学2022届高三下学期开学考试数学试题