名校
解题方法
1 . 有
个编号分别为1,2,…,
的盒子,第1个盒子中有3个白球1个黑球,其余盒子中均为1个白球1个黑球,现从第1个盒子中任取一球放入第2个盒子,再从第2个盒子中任取一球放入第3个盒子,以此类推,从第
个盒子中取到白球的概率是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2 . 记正项数列
的前
项和为
,若
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57deda4866b0d5825402b9153cdd6b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a83bd56182758d8ef1e15eb5ad3dd9f.png)
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2024-05-16更新
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2卷引用:重庆康德卷2024年普通高等学校招生全国统一考试高三第二次联合诊断考试数学试题
名校
解题方法
3 . 不经过第四象限的直线
与函数
的图象从左往右依次交于三个不同的点
,
,
,且
,
,
成等差数列,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4c6592bbbee1498da630bd431299fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132668fc41c8266ba917dc5b4995c6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0a4d02005ed2c048b59856ad98c030.png)
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2024-05-14更新
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216次组卷
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2卷引用:重庆市第一中学校2023-2024学年高二下学期5月月考数学试题
4 . 甲口袋中装有2个黑球和1个白球,乙口袋中装有3个白球.现从甲、乙两口袋中各任取一个球交换放入另一口袋,重复
次这样的操作,记甲口袋中黑球个数为
,恰有2个黑球的概率为
,恰有1个黑球的概率为
,则
的数学期望![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73fc94576d43a3f2d941e26e3295fe24.png)
________ .(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce603aa3abcb61750d2191aaa13dddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73fc94576d43a3f2d941e26e3295fe24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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5 . 将杨辉三角中的每一个数
都换成分数
,就得到一个如图所示的分数三角形,称为莱布尼茨三角形,从莱布尼茨三角形可以看出:
,令
,
是
的前n项和,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb4fb20d3a3a67baa8505623e0bd9de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f2b94b78505bbc9a08ab0b4c3366fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f15150e25e6987b44e131991caa1d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9abb647fd7ac1ee888183e01e554234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
|
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6 . 如图,正方形
的边长为1,连接
各边的中点得到正方形
,连接正方形
各边的中点得到正方形
,依此方法一直进行下去.记
为正方形
的面积,
为正方形
的面积,
为正方形
的面积,……..
为
的前
项和.给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/c953b28a-410f-4e09-8ec2-bc4ac20a0ddb.png?resizew=142)
①存在常数
,使得
恒成立;②存在正整数
,当
时,
;③存在常数
,使得
恒成立;④存在正整数
,当
时,
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a8012195f63ecbb610ba810a806103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a8012195f63ecbb610ba810a806103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/c953b28a-410f-4e09-8ec2-bc4ac20a0ddb.png?resizew=142)
①存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ca7e3eede8f49b5aeec8f21dfe5411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f36a43e6b2660feaf82c88db905ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4eadb6761fe3c3c8dde8bdb1631e40e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f555bcf970e76c33f66e2cbc4a11764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ef124353a6e8f7a699086e5fd8e329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c751cf56508033b752972ffaec70121f.png)
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2024-01-19更新
|
262次组卷
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3卷引用:重庆市万州二中教育集团2023-2024学年高二下学期入学质量监测数学试题
重庆市万州二中教育集团2023-2024学年高二下学期入学质量监测数学试题北京市东城区2023-2024学年高二上学期期末统一检测数学试卷(已下线)第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
7 . 记
上的可导函数
的导函数为
,满足
的数列
称为“牛顿数列”.若函数
,且
,数列
为牛顿数列.设
,已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
______ ,数列
的前
项和为
,若不等式
对任意的
恒成立,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33610d2a46105e3c8456257221d3d07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2b53cd9892f6d174509740afbc69d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc99d88113ea15551836c088b344556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192c4daedc8900415241cc1717a279f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd2d9c376d608c2a5cef50e0acd006f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38f76ec3596e138bcc09945c6fbde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2024-02-04更新
|
874次组卷
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10卷引用:重庆市第八中学校2023-2024学年高三上学期高考适应性月考(三)(11月)数学试题
重庆市第八中学校2023-2024学年高三上学期高考适应性月考(三)(11月)数学试题重庆市沙坪坝区重庆八中2024届高三上学期高考适应性月考卷(三)数学试题(已下线)山东省济南市2022-2023学年高三上学期期中数学试题变式题15-18(已下线)考点16 几类特殊的数列模型 2024届高考数学考点总动员【练】(已下线)大招6 数列函数属性湖北省武汉市华中师范大学第一附属中学2023-2024学年高二上学期期末检测数学试题湖南省张家界市2023-2024学年高二上学期期末联考数学试题江苏省盐城市东台市安丰中学等六校2024届高三下学期4月联考数学试题湖北省部分高中联考协作体2023-2024学年高二下学期期中考试数学试卷(已下线)【讲】专题4 数列新定义问题
名校
解题方法
8 . 从教学楼一楼到二楼共有11级台阶(从下往上依次为第1级,第2级,
,第11级),学生甲一步能上1级或2级台阶,若甲从一楼上到二楼使用每一种方法都是等概率的,则甲踩过第5级台阶的概率是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
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2023-12-23更新
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1091次组卷
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4卷引用:重庆市乌江新高考协作体2024届高考模拟监测(一)数学试题
重庆市乌江新高考协作体2024届高考模拟监测(一)数学试题安徽省皖豫名校联盟2024届高中毕业班第二次联考数学试题(已下线)考点11 由实际问题探究递推关系 2024届高考数学考点总动员【练】(已下线)模块八 概率与统计(测试)
名校
9 . 已知数列
,对任意正整数
,
,
,
成等差数列,公差为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acca5aa6b2285d897a65c289c1b54ba.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c0062e5a519fd16ebe52ff2ba086b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7b6ecfdff9d2b29ef64d2a6f3343f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069c88b849f37a1597cb7e9cdcb1e755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acca5aa6b2285d897a65c289c1b54ba.png)
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2023-11-16更新
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3卷引用:重庆市北碚区西南大学附中2024届高三上学期11月模拟测试数学试题
名校
解题方法
10 . 已知无穷等差数列
中的各项均大于0,且
,则
的范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab388c95d9ee9571855eb3958cae4ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43be0c3c40c33b7c424e89a10e0a0d41.png)
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2023-10-11更新
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3卷引用:重庆实验外国语学校2024届高三上学期10月月考数学试题