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)
您最近一年使用:0次
2 . 已知数列
满足
,
.
(1)证明:数列
为等比数列;
(2)在
与
之间插入
个数,使得这
个数组成公差为
的等差数列,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57bfc1f8772f31748bfdc280d0712fc0.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4792fd59c4ca11ff03dc32e367c3983f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d1ae060458f733025fc82f7c7b14f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
今日更新
|
275次组卷
|
4卷引用:河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题
名校
解题方法
3 . 已知数列
的前n项和为
,
,
,
.
(1)求数列
和
的通项公式;
(2)记数列
的前n项和为
,若
对任意
都成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65c44af8125cfd1e8c9a6d2985bcee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4aede2d0a9e7eb471b709438d11d4a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83de9a45d9b680da8835bac1fee9c9b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bde034b0bb6767f923526db8a387c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b8a237d8f9dc2d57db4e8bea895796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
您最近一年使用:0次
名校
4 . 在活动中,初始的袋子中有5个除颜色外其余都相同的小球,其中3个白球,2个红球.每次随机抽取一个小球后放回.规则如下:若抽到白球,放回后把袋中的一个白球替换为红球;若抽到红球,则把该红球放回袋中.记经过
次抽取后,袋中红球的个数为
.
(1)求
的分布列与期望;
(2)证明
为等比数列,并求
关于
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8dfeb1a37fe9ebefefd522a7c582e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46931d3b33e64b09805b43b4d0da253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685a18e8694ab2c3243133d8a1988e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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7日内更新
|
468次组卷
|
7卷引用:江西省部分学校2023-2024学年高二下学期第二次月考(5月联考)数学试题
名校
解题方法
5 . 在边长为3的正方形ABCD中,作它的内接正方形EFGH,且使得
,再作正方形EFGH的内接正方形MNPQ,使得
依次进行下去,就形成了如图所示的图案.设第
个正方形的边长为
(其中第1个正方形的边长为
,第2个正方形的边长为
),第
个直角三角形(阴影部分)的面积为
(其中第1个直角三角形AEH的面积为
,第2个直角三角形EQM的面积为
,)则下列结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad509828b6e956a21af18d44bb6132a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01d966ba6d020568cde41cf18d94d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6726b4835be2c778dcedb27e3373654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6faf5a934175781d88799af881ef47.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/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669ae8d3bf90758caed001bc01e2fa14.png)
A.![]() | B.![]() |
C.数列![]() ![]() ![]() ![]() | D.数列![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知数列
的前
项和为
,满足
.记
为数列
在区间
内的项的个数,则数列
的前100项的和为_____________ .
![](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/77ea9f7f80c70ca4a52a050f1d05da09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e8510cf4a62bccaa7d56e46c1c16c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
您最近一年使用:0次
名校
解题方法
7 . 已知
是等比数列,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf334b1e8cef2312c4c2b918b3e59236.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba9dc6fb3fee2f98c8177d837f00d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf334b1e8cef2312c4c2b918b3e59236.png)
您最近一年使用:0次
名校
解题方法
8 . 数列
的前
项和
,数列
满足
,
.
(1)求
,
;
(2)记
,求数列
的前
项和
.
![](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/4300dca231e2f4b37f70900b33439d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aef1f4bc64726253be1e2f83b00630d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a36c2f125bc8b3be4ffd62e8e41e96.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e5a2a15b63514bf4286faceab803c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
解题方法
9 . 记数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)设
,证明:
.
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97db527fd3d74206b20df0f5ec318bbf.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c60af883387104aefde8d845676dcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318701b52d3102cae111b54f1b0360ac.png)
您最近一年使用:0次
10 . 已知等差数列
与正项等比数列
满足
,且
,20,
既是等差数列,又是等比数列.
(1)求数列
和
的通项公式;
(2)若
,数列
的前n项和
,满足对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85444874c705666de9488286d3d61dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161a7b35d1812e6745ae7f7c540cf87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c969826f605d65fcf0f7ecf2ff49d4c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbfef1a3822e45dbac592fca07e9f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-06-05更新
|
467次组卷
|
2卷引用:湖北省云学名校联盟2023-2024学年高二下学期5月联考数学试题A卷