名校
解题方法
1 . 已知
是正项数列
的前
项和,满足
,
.
(1)若
,求正整数
的值;
(2)若
,在
与
之间插入
中从
开始的连续
项构成新数列
,即
为
,求
的前30项的和.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7d4d436a8f90d940078a5bb900c12b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb225c17c6055dae4c8d0cdc20f2a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6f89b70392f9cedcffd8bdc953824c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c7688fdbb166d2171c9b952d09c7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09356eb4b6e7fe090f3e4dc8158bf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8aa0dfca3e2ae79d39b50afff50d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739520f056a75b3a90f7d485bf61f8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2023-11-24更新
|
786次组卷
|
3卷引用:江西省部分地区2023-2024学年高三上学期11月质量检测数学试题
2 . 已知数列
满足:对任意正整数
,都有
.
(1)若
,求
的值;
(2)设
,且
,求证:
是等差数列,并求
的前
项和;
(3)若
是公比为
的等比数列,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94628ebd7617a39f9ea4fc6f4926da6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648d19bdfb3fcb554e3756b438746602.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73220418267b9ac7f86efd73392c5789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e42a8394334f1a76bf828667fc5f2b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3986f143e29091c74896bfe21fb41dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2938c6ad0d60a4decc198c8a3c63ca7.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)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
您最近一年使用:0次
名校
解题方法
3 . 马尔科夫链是概率统计中的一个重要模型,也是机器学习和人工智能的基石,在强化学习、自然语言处理、金融领域、天气预测等方面都有着极其广泛的应用.其数学定义为:假设我们的序列状态是…,
,
,
,
,…,那么
时刻的状态的条件概率仅依赖前一状态
,即
.
现实生活中也存在着许多马尔科夫链,例如著名的赌徒模型.
假如一名赌徒进入赌场参与一个赌博游戏,每一局赌徒赌赢的概率为
,且每局赌赢可以赢得1元,每一局赌徒赌输的概率为
,且赌输就要输掉1元.赌徒会一直玩下去,直到遇到如下两种情况才会结束赌博游戏:一种是手中赌金为0元,即赌徒输光;一种是赌金达到预期的B元,赌徒停止赌博.记赌徒的本金为
,赌博过程如下图的数轴所示.
,
)时,最终输光的概率为
,请回答下列问题:
(1)请直接写出
与
的数值.
(2)证明
是一个等差数列,并写出公差d.
(3)当
时,分别计算
,
时,
的数值,并结合实际,解释当
时,
的统计含义.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddb0beac0bd710c60a40ec6c54e57dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f6244120cc13347c5510e58fc6dda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb150b73ea7c87972a0b57510a99472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b49fdb5924134bfc54266f0fee35ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b49fdb5924134bfc54266f0fee35ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb150b73ea7c87972a0b57510a99472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae9ac04464a40eb69a5fae420813094.png)
现实生活中也存在着许多马尔科夫链,例如著名的赌徒模型.
假如一名赌徒进入赌场参与一个赌博游戏,每一局赌徒赌赢的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1065ae0947705c7d16a5a86c78f07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1065ae0947705c7d16a5a86c78f07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67842f237b7dc20ea35d01f293dc33ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87caad7560feb72d6ab5ee901a81c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6291d7b91f71daa0b3c4fa02dc7a5ea.png)
(1)请直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba837ccb2f36f9dcef19706e5a1f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108ab49f370919e730e3567070deee65.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d609340751d14a19ec77c14b8e2b961d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf47b8e265017c3a85fe62885cfe326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00ab7fda9966e69ae783a3c634fcd46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74eb955982bcd3bc52ba54ab0f69a565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c94b61a898a318846e6d30b85d5a637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
您最近一年使用:0次
2023-04-06更新
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11048次组卷
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21卷引用:江西省景德镇一中2022-2023学年高二(19班)下学期期中考试数学试题
江西省景德镇一中2022-2023学年高二(19班)下学期期中考试数学试题广东省珠海市第二中学2023-2024学年高二下学期期中考试数学试题浙江省杭州市2023届高三下学期教学质量检测(二模)数学试题(已下线)专题10 计数原理与概率统计(理科)(已下线)模块二 专题4 条件概率与全概率公式(已下线)专题08 概率统计及计数原理(已下线)押新高考第19题 概率统计湖南师范大学附属中学2023届高三三模数学试题(已下线)第四篇 概率与统计 专题6 随机游走与马尔科夫过程 微点1 随机游走与马尔科夫链广东省佛山市南海区第一中学2024届高三上学期10月月考数学试题(已下线)重难点突破01 概率与统计的综合应用(十八大题型)-3(已下线)概 率辽宁省沈阳市第二中学2024届高三下学期开学考试数学试题专题14条件概率与全概率公式(已下线)专题03 条件概率与全概率公式(2)(已下线)专题04 概率统计大题(已下线)专题8-2分布列综合归类-2(已下线)湖南省郴州市2024届高三一模数学试题变式题17-22(已下线)专题6 全概率与数列结合问题河南省信阳市新县高级中学2024届高三下学期适应性考试(八)数学试题单元测试B卷——第七章 随机变量及其分布
名校
解题方法
4 . 已知数列
满足:
,
,
,3,4,…,则下列说法正确的是( )
![](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/b039543372ce127c7b85782a118f0f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
A.![]() |
B.对任意![]() ![]() |
C.不存在正整数![]() ![]() ![]() ![]() ![]() ![]() |
D.数列![]() |
您最近一年使用:0次
2022-11-14更新
|
1056次组卷
|
5卷引用:山东省青岛市西海岸新区2022-2023学年高二上学期期中学业水平检测数学试题
名校
5 . 若数列
的子列
均为等差数列,则称
为k阶等差数列.
(1)若
,数列
的前15项与
的前15项中相同的项构成数列
,写出
的各项,并求
的各项和;
(2)若数列
既是3阶也是4阶等差数列,设
的公差分别为
.
(ⅰ)判断
的大小关系并证明;
(ⅱ)求证:数列
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6445438ad302d53a1a94d36d1348f9b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c15034b5b5cb8ca7ef64bb7517a19a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5708191e2a4453461ea398c4e16ab6.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/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7b0cec593a0ea2980b968d3aa826e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367c96a0ff95b92877eda2a7c98871e1.png)
(ⅰ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367c96a0ff95b92877eda2a7c98871e1.png)
(ⅱ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2022-11-02更新
|
460次组卷
|
3卷引用:北京市大兴区2023届高三上学期期中检测数学试题
名校
6 . 设
为正整数,若无穷数列
满足
,则称
为
数列.
(1)数列
是否为
数列?说明理由;
(2)已知
其中
为常数.若数列
为
数列,求
;
(3)已知
数列
满足
,
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f368487239b6fcc20a8d9bdc0867a099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb9b392b1c516e66242727dd9c055f5.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f367d90f02b00f728b0d64c03a9397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e99810c3a6990151d49592015b4f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171a37e4d0bf1ef80a57e8349e8e3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7f86cdde6bf669dd3fb53b7f952272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
2022-03-29更新
|
1848次组卷
|
10卷引用:上海市七宝中学2022届高三下学期期中数学试题
上海市七宝中学2022届高三下学期期中数学试题(已下线)高二下期中真题精选(压轴40题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)北京市第五十七中学2023-2024学年高一1+3下学期期中考试数学试卷北京市海淀区2022届高三一模数学试题(已下线)数学-2022年高考押题预测卷01(北京卷)北京市第八中学2023届高三上学期10月月考数学试题(已下线)北京市海淀区2022届高三一模数学试题变式题17-21(已下线)模块九 数列-2北京卷专题18数列(解答题)
名校
解题方法
7 . 已知数列
满足:
,
,其前
项和为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bab579028a0ef0bd361c19b53d4995b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2021-11-29更新
|
1247次组卷
|
5卷引用:重庆市巴蜀中学2021-2022学年高二上学期期中数学试题
重庆市巴蜀中学2021-2022学年高二上学期期中数学试题(已下线)专题4.8 数列(能力提升卷)-2021-2022学年高二数学特色专题卷(人教A版2019选择性必修第二册)重庆市铁路中学2021-2022学年高二上学期12月月考数学试题2023版 湘教版(2019) 选修第一册 过关斩将 全书综合测评河北省沧州市任丘市第一中学2021-2022学年高二上学期第三次阶段考数学试题
解题方法
8 . 如图所示,四边形
是平行四边形,过点
的直线与射线
、
分别相交于点
、
,若
,
.
![](https://img.xkw.com/dksih/QBM/2021/4/16/2701196987301888/2790360975630336/STEM/62fac8bd-0356-4b95-94e5-2d1ac8ac7b16.png?resizew=341)
(1)把
用
表示出来(即求
的解析式);
(2)设数列
的首项
,前
项和
满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39758894bf29f5c85e76dc924b6db834.png)
,求数列
通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f68923146cb9aa2fec930b91fdc9b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1992fe65cd5c5cbbcfe95e370072d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcae23616b928078169005f69e934722.png)
![](https://img.xkw.com/dksih/QBM/2021/4/16/2701196987301888/2790360975630336/STEM/62fac8bd-0356-4b95-94e5-2d1ac8ac7b16.png?resizew=341)
(1)把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/39758894bf29f5c85e76dc924b6db834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd048fe3fbd6b0623f146a0ef9021e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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