名校
1 . 学校食堂每天中午都会提供
两种套餐供学生选择(学生只能选择其中的一种),经过统计分析发现:学生第一天选择
套餐概率为
,选择
套餐概率为
;而前一天选择了
套餐的学生第二天选择
套餐的概率为
,选择
套餐的概率为
;前一天选择
套餐的学生第二天选择
套餐的概率为
,选择
套餐的概率也是
;如此反复,记某同学第
天选择
套餐的概率为
,选择
套餐的概率为
;5个月(150天)后,记甲、乙、丙三位同学选择
套餐的人数为
,则下列说法中正确 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7日内更新
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525次组卷
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5卷引用:【江苏专用】高二下学期期末模拟测试B卷
(已下线)【江苏专用】高二下学期期末模拟测试B卷广东省四会中学、广信中学2023-2024学年高二下学期第二次联考数学试题(已下线)【讲】 专题三 复杂背景的概率计算问题(压轴大全)山东省烟台市牟平区第一中学2023-2024学年高二下学期6月限时练(月考)数学试题河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
解题方法
2 . 正三棱柱
的底面边长为1,侧棱长为2,一只蚂蚁从
点出发,每次沿着该三棱柱的一条棱的端点爬行到另一个端点,若它选择三个方向爬行的概率相等,且每次爬行都相互独立.
(1)记这只蚂蚁经过4次爬行后,其爬行的总路程为
,求
的分布列和数学期望;
(2)求这只蚂蚁经过5次爬行后,停留在平面
内的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)记这只蚂蚁经过4次爬行后,其爬行的总路程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)求这只蚂蚁经过5次爬行后,停留在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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名校
3 . 已知数列
的各项均为正整数,设集合
,记T的元素个数为
.
(1)若数列
,且
,
,求数列
和集合T;
(2)若
是递增的等差数列,求证:
;
(3)请你判断
是否存在最大值,并说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53a75cc8bb3e86ce991461f49c68d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce7cbd168eba6d06fed9dc80417fd6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c20b965367feba4ef99a52d196a707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc668d959b811bef55a1e672eb1dcec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f255d89ed61b51eb161d74e518b9a763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be63af01fc637c108801b34882acc1a4.png)
(3)请你判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
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名校
解题方法
4 . 杨家坪中学足球社团是一个受学生欢迎的社团,社团中的甲、乙、丙三名成员将进行传球训练,从甲开始随机地将球传给其他两人中的任意一人,接球者再随机地将球传给其他两人中的任意一人,如此不停地传下去,且假定每次传球都能被接到,记开始传球的人为第
次触球者,第
次触球者是甲的概率记为
,即
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](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/45e03e7f8bdd53063fdccec3c99f9ac2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知离散型随机变量
服从二项分布
,其中
,记
为奇数的概率为
,
为偶数的概率为
,则下列说法中不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66562230293975e4ac391943ae62054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d787593ec73d53b1504397cabe532d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
A.![]() | B.![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
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6 . 我国南宋数学家杨辉
年所著的《详解九章算法》给出了著名的杨辉三角,由此可见我国古代数学的成就是非常值得中华民族自豪的,下图是由 “杨辉三角”拓展而成的三角数阵,记第一条斜线之和为
,第二条斜线之和为
,第三条斜线之和为
,以此类推,组成数列
.例如
若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9226d42c0e35c51c7118a27fd62b07.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/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e66cc2ad8242b7e1e29e94196740d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8bb0c4e75487e50e354a14ca0fdece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
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解题方法
7 . 已知数列
满足
,
.
(1)证明:数列
为等差数列,并求数列
的通项公式;
(2)若记
为满足不等式
的正整数k的个数,设数列
的前n项和为
,求关于n的不等式
的最大正整数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ad6c0066bd2593d37a0b6b762b7c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b01041691ad489f126f05c18ea8f0fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4680e5e9a6995b82006bde3e8ed402f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45dac5ff2e7b2d374df06d240b5839e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4796ab389935d763a3db9a012d1df3.png)
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2024-04-22更新
|
600次组卷
|
14卷引用:江苏省镇江市扬中高级中学2022-2023学年高二上学期期末数学试题
江苏省镇江市扬中高级中学2022-2023学年高二上学期期末数学试题(已下线)江苏省南通市如皋市2022-2023学年高三上学期10月诊断调研测试数学试题(已下线)江苏省南通市如皋市2022-2023学年高三上学期期中模拟数学试题(已下线)吉林省长春市长春吉大附中实验学校2023-2024学年高二上学期1月期末数学试题(已下线)期末真题必刷压轴60题(23个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)专题09 数列求和6种常见考法归类(3)山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题四川省都江堰中学2019-2020学年高一下学期期中数学试题(已下线)专题4.6 《数列》单元测试卷(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A版,浙江专用)福建省厦门市厦门外国语学校2023届高三上学期期中考试数学试题吉林省长春市长春吉大附中实验学校2022-2023学年高三上学期第四次摸底考试数学试题(已下线)专题1 数列的单调性 微点3 数列单调性的判断方法(三)——倒数比较法(已下线)4.3.2 等比数列的前n项和公式——课后作业(巩固版)(已下线)数列-综合测试卷A卷
解题方法
8 . 已知数列
是等差数列,数列
是公比大于1的等比数列,
的前
项和为
.条件①
;条件②
;条件③
;条件④
.从上面四个条件中选择两个作为已知,使数列
、
存在且唯一确定.
(1)求数列
、
的通项公式;
(2)求数列
的前
项和
.
![](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/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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec4a0a0e86d0bed8a4ec0843630507ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02df18fb5229ea848c7786da745edee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb9a4dc75c66bb58fab0d0ffc0bfe15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac855db4c060db39c16f7e59da60167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
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解题方法
9 . 设等差数列
的前n项和为
,数列
的前
项和为
.若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec07ef49aef97877d22356694ceb7d.png)
_____________ .
![](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/4dea1dd4ffcb4cf0697ca43079f6a1f2.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/1ba446d4f40ad7eb438811c23625f708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dff0c72be75873631dc3a83ea67c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec07ef49aef97877d22356694ceb7d.png)
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10 . 已知等比数列
的各项均为正数,若
,
,则
( )
![](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/28d84ee688592caf22e84910db79e7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
A.1 | B.2 | C.![]() | D.![]() |
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