名校
1 . 若项数为
的数列
满足:
,且存在
,使得
,则称数列
具有性质P.
(1)①若
,写出所有具有性质P的数列
;
②若
,写出一个具有性质P的数列
;
(2)若
,数列
具有性质P,求
的最大项的最小值;
(3)已知数列
均具有性质P,且对任意
,当
时,都有
.记集合
,
,求
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adcce353c3ced76645069760bdf8fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad107fc0e55e4b35b2b25b10f75f4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96b51d9b57fb8f9577f575261c08206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0265ce589cdf60588c9f86671a256992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc147c3c0863d22533a820cc469bfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818b44478f6d1d972aa5bf6dd4d3a0c.png)
(1)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a215612787e43d28bfebc840c3903b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1ddc5b7f288c044f394fd7055e2564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7aa41f0d2bd18825f741a3cc2adef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645ae0b78ad4ca300e3889ca3f9bcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645ae0b78ad4ca300e3889ca3f9bcce.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719c07413b9a867b83f27f5eed752846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6119a01b55a29adabf43ddb2a5211e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0504794eebd6814a3138e796666bca01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191929f42f9053e7355a1a9068ba072f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5975dbb4789b4b2d8f2f0eb3abb4da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc47ee887b63cdc46fdb17dcb75f2f4.png)
您最近一年使用:0次
2023-06-01更新
|
716次组卷
|
3卷引用:北京师范大学附属实验中学2023届高三三模数学试题
名校
解题方法
2 . 如图,点
均在
轴的正半轴上,
,
,…,
分别是以
为边长的等边三角形,且顶点
均在函数
的图象上.
个等边三角形的边长
;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e670062f54fef9f2af635014f22c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb99c20237aca8ff2ba640c28fbc5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a619e2751f422ae187505e95339d02fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b80801bd92f36541707eea1229685e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43534ea1b9c007f961148b68e2adad1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02163d48486b66a17dd434e57877cc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cfa1efc047521bc9f9b60ab3122752.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
2024-06-08更新
|
662次组卷
|
2卷引用:四川省凉山州2024届高三第三次诊断性检测数学(理)试题
名校
3 . 某运动员多次对目标进行射击, 他第一次射击击中目标的概率为
.由于受心理因素的影响,每次击中目标的概率会受前一次是否击中目标而改变,若前一次击中目标,下一次击中目标的概率为
;若前一次末击中目标,则下一次击中目标的概率为
.
(1)记该运动员第
次击中目标的概率为
,证明:
为等比数列,并求出
的通项公式;
(2)若该运动员每击中一次得2分,未击中不得分,总共射击2次,求他总得分
的分布列与数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)记该运动员第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0fd459ceae1ed8a031ab462546d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5a325806df1a1c3e7ce609fe99085f.png)
(2)若该运动员每击中一次得2分,未击中不得分,总共射击2次,求他总得分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
2022-09-23更新
|
1312次组卷
|
4卷引用:云南师范大学附属中学2023届高三上学期适应性月考卷(三)数学试题
4 . 晋中市是晋商文化的发源地,且拥有丰富的旅游资源,其中有保存完好的大院人文景观(如王家大院,常家庄园等),也有风景秀丽的自然景观(如介休绵山,石膏山等).某旅行团带游客来晋中旅游,游客可自由选择人文景观和自然景观中的一处游览.若每位游客选择人文景观的概率是
,选择自然景观的概率为
,游客之间选择意愿相互独立.
(1)从游客中随机选取5人,记5人中选择人文景观的人数为X,求X的均值与方差;
(2)现对游客进行问卷调查,若选择人文景观记2分,选择自然景观记1分,记已调查过的累计得分为n分的概率为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)从游客中随机选取5人,记5人中选择人文景观的人数为X,求X的均值与方差;
(2)现对游客进行问卷调查,若选择人文景观记2分,选择自然景观记1分,记已调查过的累计得分为n分的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
您最近一年使用:0次
5 . 给定整数
,对于数列
定义数列
如下:
,
,其中
表示
,
这
个数中最小的数.记
.
(1)若数列
为①1,0,0,1;②1,2,3,4,5,6,7,分别写出相应的数列
;
(2)求证:若
,则有
;
(3)若
,常数
使得
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b686ebe4e3a65d19992d84f4fa76b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4068255c1a5d37d57a6da090c775351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f63c86fcfa5c0b4715fbda9f828283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f7ab4162be6cc63ed97eabb6ba9d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2326369afa2fc4bc629efd88ac8950d9.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求证:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbaa88539a7d77c011f3dd4d64b251af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2617515e5ce81b3f5d9f4e806b21b0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547343b443dba2d77da457f77c21b204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2e736950c3a8de5083b5c60d46e84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
您最近一年使用:0次
2023-07-17更新
|
591次组卷
|
5卷引用:北京市海淀区2022-2023学年高二下学期学业水平调研(期末)数学试题
北京市海淀区2022-2023学年高二下学期学业水平调研(期末)数学试题山东省潍坊市临朐县第一中学2023-2024学年高二下学期3月月考数学试题山东省青岛市第五十八中学2023-2024学年高二下学期阶段性(4月)模块检测数学试卷【北京专用】专题03数列(第三部分)-高二上学期名校期末好题汇编(已下线)专题02 等比数列4种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北京专用)
6 . 国际象棋是国际通行的智力竞技运动.国际象棋使用
格黑白方格相间棋盘,骨牌为每格与棋盘的方格大小相同的
格灰色方格.若某种黑白相间棋盘与骨牌满足以下三点:①每块骨牌覆盖棋盘的相邻两格;②棋盘上每一格都被骨牌覆盖;③没有两块骨牌覆盖同一格,则称骨牌构成了棋盘的一种完全覆盖.显然,我们能够举例说明
格黑白方格相间棋盘能被骨牌完全覆盖.
格黑白方格相间棋盘的对角两格,余下棋盘不能被骨牌完全覆盖;
(2)请你切掉
格的黑白方格相间棋盘的任意两个异色方格,然后画出余下棋盘的一种骨牌完全覆盖方式,并证明:无论切掉的是哪两个异色方格,余下棋盘都能被骨牌完全覆盖;
(3)记
格黑白方格相间棋盘的骨牌完全覆盖方式数为
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb79f6535ee15a3d41ca71cf72082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(2)请你切掉
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5d94e748101eaf9aa5ae725b0040e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485596f7fc2aa8d80466a7d02a00af15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cfd722654be25b48b28ba0f6698e89.png)
您最近一年使用:0次
2024-03-06更新
|
791次组卷
|
4卷引用:山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题
山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题(已下线)第四套 最新模拟重组卷江苏省苏州大学2024届高考新题型2月指导卷数学试题(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总
名校
解题方法
7 . 记
,已知数列
和
分别满足:
.
(1)求
的通项公式;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef8ea6000c6642f61f1f83483b22966.png)
![](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/6822862220a0efe09dc4158ea7ec0539.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96cc6cd76e1f5bcfe2e4847ab422bb8.png)
您最近一年使用:0次
2023-02-26更新
|
605次组卷
|
3卷引用:浙江省宁波市慈溪市2022-2023学年高二上学期2月期末数学试题
8 . 已知数列
的前
项和为
.
从下面①②③中选择其中一个作为条件解答试题,若选择不同条件分别解答,则按第一个解答计分.
①数列
是等比数列,
,且
,
,
成等差数列;
②数列
是递增的等比数列,
,
;
③
.
(1)求数列
的通项公式;
(2)已知数列
的前
项的和为
,且
.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/08eb71ecf8d733b6932f4680874dbbf3.png)
从下面①②③中选择其中一个作为条件解答试题,若选择不同条件分别解答,则按第一个解答计分.
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f7519e1b1dd927bc634eedafc88820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b32aee86109b777671cd62868db3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86e2e42b4aa93db9241103e7f61766c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1054571e0bc599d64a89b63a49b574df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdefe767533b3368858d21233e65bf59.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8370a173854471a3eb27637993a3d5d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca47592031bf780a3b7a784f34f851b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
2022-03-01更新
|
1323次组卷
|
6卷引用:辽宁省沈阳市大东区2022届高三下学期质量监测数学试题
辽宁省沈阳市大东区2022届高三下学期质量监测数学试题山东省淄博市2021-2022学年高二下学期期中数学试题(已下线)第四章 数列(A卷·知识通关练) (3)(已下线)模块一 专题6《数列的通项公式与求和问题》单元检测篇 A基础卷(已下线)模块一专题2《数列的通项公式与求和》单元检测篇A基础卷(高二人教B版)(已下线)模块一 专题3《数列的通项公式与求和》单元检测篇A基础卷(高二北师大版)
名校
9 . 设正整数数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fcec9111f2e905229ace48be2ca6f.png)
.
(1)若
,请写出
所有可能的取值;
(2)记集合
,证明:若集合
存在一个元素是3的倍数,则
的所有元素都是3的倍数;
(3)若
为周期数列,求
所有可能的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fcec9111f2e905229ace48be2ca6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34434a0b7330efb26ef92e8e86301fd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d8c8d85bc63a7fca39acb0442ff167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21550abb7c545b53cd2336a7a76885fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
2022-04-14更新
|
1301次组卷
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6卷引用:北京市顺义区2022届高三第二次统练数学试题
北京市顺义区2022届高三第二次统练数学试题北京市一零一中学2022届高三下学期三模数学试题(已下线)考点15 数列综合问题-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)北京一零一中学2023届高三下学期开学考数学试题(已下线)北京市第四中学2024届高三上学期10月月考数学试题变式题16-21(已下线)专题04 数列(5)
2023高三·全国·专题练习
解题方法
10 . 已知抛物线
与点
,过点
作切线
(
为切点),取点
满足
;过点
作切线
(
为切点),取点
满足
;…依次得到点列
,
,…,
,数列
为单调数列.
(1)求
,
.
(2)证明:
.
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ad7c068b9b7c0fd764cf7746407079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3169b9e651cfe7c781ab1cd05836065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56f2e56229a722d1f40d74d3967a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89af7170bb5cff9869993aa05c62220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e2d739c9ab27e84464962035775a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2857fac4963b129d99e79dcb3e13d295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0dc36ca4fdb257fb296cf0b9234eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042f6277c98e108cab95992342e4bfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09490514476657414d8991d633c9d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c5b2ecf3d4a067272790f360b5d05d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cc7e43a26e8bafbc6c02eb619bea9.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba46062609219b82c694ed3776fde0ad.png)
您最近一年使用:0次