1 . 如图有标号为1,2,3的三根柱子,在1号柱子上套有
个金属圆片,从下到上圆片依次减小.按下列规则,把金属圆片从1号柱子全部移到3号柱子,要求:①每次只能移动一个金属圆片;②较大的金属圆片不能在较小的金属圆片上面.(1)若
时,至少需要移动______ 次;(2)将
个金属圆片全部移到3号柱子,至少需要移动______ 次.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2020/7/20/2510021193916416/2511218922463233/STEM/f4bfb4b5a8804b0d9e1e522367ce8aee.png?resizew=223)
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4卷引用:华大新高考联盟名校2020届高三押题考试理科数学试题
华大新高考联盟名校2020届高三押题考试理科数学试题湖北省武汉市华中师范大学第一附属中学2020届高三下学期高考押题考试理科数学试题(已下线)考点63 推理(练习)-2021年高考数学复习一轮复习笔记湖南省常德市第二中学2020-2021学年高二(332班)下学期期末数学试题
2 . 已知
,
,
,
,……照此规律
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0bfaed2a001cc6a90ab3c697514f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa23f21bdf671961f26adbd35a9502a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9525e204d37a4bcb8184500220a87c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62fd36bd582968be82ccd10721832dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd9e147903d7b2b3577d0dbcba3ec1b.png)
A.45 | B.-45 | C.55 | D.-55 |
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2020-07-19更新
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2卷引用:黑龙江省哈尔滨师范大学附属中学2020届高三下学期第三次模拟数学(文)试题
3 . 观察下列一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4f060891b422aa6ba9a0384db32cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2932125fc247617fc547bdf8a06600c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9eb4da6bb1220507fe6cf2ce593183.png)
…
则
从左到右第三个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4f060891b422aa6ba9a0384db32cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2932125fc247617fc547bdf8a06600c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9eb4da6bb1220507fe6cf2ce593183.png)
…
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066bed69d03aee63a37e1259f6599e55.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-07-16更新
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4卷引用:陕西省宝鸡市渭滨区2019-2020学年高二下学期期末数学(文)试题
4 . 已知集合
,将
中的正整数从小到大排列为:
,
,
,….若
,则正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8460b6c1099b5695d4278c2840ed61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b555c7b1ca0deed6bf9b547c38582190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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5 . 一个数字生成器,生成规则如下:第1次生成一个数
,以后每次生成的结果是将上一次生成的每一个数
生成两个数,一个是
,另一个是
.若
,前
次生成的所有数 中不同的数的个数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be6f009bfb61b11e4f87edb4132de3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8314e2f98928b76d7fb74b09283f3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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2卷引用:上海市上海中学2019-2020学年高一下学期期末数学试题
6 . 对
个不同的实数
、
、
、
可得
个不同的排列,每个排列为一行写成一个
行的数阵.对第
行
、
、
、
,记
,
、
、
、
、
.
例如用
、
、
可得数阵如下,对于此数阵中每一列各数之和都是
,所以
.那么,在用
、
、
、
、
形成的数阵中,
等于( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/cbb400ba-9a7f-4fd6-8a56-4ec374971b34.png?resizew=90)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8412f5256b2b370e421c07f18cc732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8412f5256b2b370e421c07f18cc732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa42547ccb52a7553eb133c017d3f44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f169dae2c93981413a609c891ccdf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32f28576b597297366b0456044156c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e874994a3b76ee3244adc7f2d02efc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8412f5256b2b370e421c07f18cc732.png)
例如用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8353dcd0c61a4c132f6f38995416c783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085a3262799db208b6a0ef45fde6d057.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/cbb400ba-9a7f-4fd6-8a56-4ec374971b34.png?resizew=90)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-07-15更新
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771次组卷
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3卷引用:山东师范大学附属中学2020届高三6月模拟检测数学试题
名校
7 . 下图中(1)(2)(3)(4)为四个平面图形,表中给出了各平面图形中的顶点数、边数以及区域数.
![](https://img.xkw.com/dksih/QBM/2020/7/11/2503782400442368/2505596746555392/STEM/707878b3-e8a2-4471-9937-1ef15d6c86df.png?resizew=526)
现已知某个平面图形有1009个顶点,且围成了1006个区域,试根据以上关系确定这个平面图形的边数为________ .
![](https://img.xkw.com/dksih/QBM/2020/7/11/2503782400442368/2505596746555392/STEM/707878b3-e8a2-4471-9937-1ef15d6c86df.png?resizew=526)
平面图形 | 顶点数 | 边数 | 区域数 |
1 | 3 | 3 | 2 |
2 | 8 | 12 | 6 |
3 | 6 | 9 | 5 |
4 | 10 | 15 | 7 |
现已知某个平面图形有1009个顶点,且围成了1006个区域,试根据以上关系确定这个平面图形的边数为
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8 . 杨辉三角,又称帕斯卡三角,是二项式系数在三角形中的一种几何排列,在我国南宋数学家杨辉所著的《评解九章算法》(
年)一书中用如图所示的三角形解释二项式乘方展开式的系数规律,现把杨辉三角中的数从上到下,从左到右依次排列,得数列:
,
,
,
,
,
,
,
,
,
,
,
,
,
,
…….记作数列
,若数列
的前
项和为
,则
=( )
![](https://img.xkw.com/dksih/QBM/2020/7/11/2503162710474752/2503881127198720/STEM/80d280aedb9840848fab17691dfdee02.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa99a11fa9079e92173593420f2715f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952cce39fdeea24d04e5a04500f76975.png)
![](https://img.xkw.com/dksih/QBM/2020/7/11/2503162710474752/2503881127198720/STEM/80d280aedb9840848fab17691dfdee02.png?resizew=180)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-07-12更新
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1730次组卷
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7卷引用:湖北省武汉市江岸区2019-2020学年高三上学期元月调研理科数学试题
湖北省武汉市江岸区2019-2020学年高三上学期元月调研理科数学试题(已下线)考点63 推理(练习)-2021年高考数学复习一轮复习笔记(已下线)3.3 二项式定理与杨辉三角(2)B提高练(已下线)专题3.2 二项式定理与杨辉三角(B卷提升篇)-2020-2021学年高二数学选择性必修第二册同步单元AB卷(新教材人教B版)宁夏银川一中2020-2021学年高二下学期期中考试数学(理)试题吉林省长春市实验中学2021-2022学年高二下学期4月月考数学试题吉林省长春市第二实验中学2022-2023学年高二上学期期末数学试题
解题方法
9 . 已知函数
,若
,
,
,则
在
上的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abaf7c253306f9dbcf43679534e23a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab7bb40f58f28c9799b20f91d15d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693500a9e10e314b42d0af9352fc06ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586a75e625280224cca9d67e4af7ce25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
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10 . 用火柴棒按如图的方法搭三角形,按图示的规律搭下去,则第100个图形所用火柴棒数为__________
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/79a81873-f72a-481e-8d89-3d9eb917a225.png?resizew=461)
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2020-07-11更新
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118次组卷
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2卷引用:黑龙江省哈尔滨师范大学附属中学2019-2020学年高二下学期期末考试数学(文)试题