1 . 对于正整数
,最接近
的正整数设为
,如
,记
,从全体正整数中除去所有
,余下的正整数按从小到大的顺序排列得到数列
,则数列
的前8项和为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d249094ecb996458e35182d6b461299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c82c7591e80b01a6fac3f7cd499514d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46752bd68b97f8cb69b26e14acdc468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2023-02-03更新
|
832次组卷
|
3卷引用:第1题 高斯函数与数列最值结合(压轴小题6月)
(已下线)第1题 高斯函数与数列最值结合(压轴小题6月)河南省驻马店市2022-2023学年高三上学期期末统一考试数学(理科)试题上海外国语大学附属浦东外国语学校2022-2023学年高二下学期期末数学试题
名校
2 . 已知有限数列
共M项
,其任意连续三项均为某等腰三角形的三边长,且这些等腰三角形两两均不全等.将数列
的各项和记为
.
(1)若
,直接写出
的值;
(2)若
,求
的最大值;
(3)若
,求
的最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091a311dffd9390d3a561bd2fd12b15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5c27df6976ecad2e7e015ee86ef8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364e6d15fe646947fdd3f622e36612dd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e081cc8f7f2b2ebcad121e628e9a9650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/789b8f82684394ecc3e6776a3305b4a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2022-05-12更新
|
1664次组卷
|
5卷引用:模块九 数列-2
(已下线)模块九 数列-2(已下线)2023年北京高考数学真题变式题16-21北京市海淀区2022届高三二模数学试题北京市海淀区北京一零一中学2023届高三上学期统考(二)数学试题北京师范大学附属中学2022-2023学年高一下学期期末考试数学试题
3 . 设
为无穷数列,给定正整数
,如果对于任意
,都有
,则称数列
具有性质
.
(1)判断下列两个数列是否具有性质
;(结论不需要证明)
①等差数列
:5,3,1,…;②等比数列
:1,2,4,….
(2)已知数列
具有性质
,
,
,且由该数列所有项组成的集合
,求
的通项公式;
(3)若既具有性质
又具有性质
的数列
一定是等差数列,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8feaf51b5fdc0b7aad38b26f57825712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575e42a3bdb429360418e949bd963a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
(1)判断下列两个数列是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
①等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f3e9d115d6290eee217a29dc399cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若既具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee83304e529e6d24ea7ff894bd6d87a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-07-10更新
|
733次组卷
|
5卷引用:高二数学下学期期末押题试卷01
(已下线)高二数学下学期期末押题试卷01【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)2024年新课标全国Ⅰ卷数学真题变式题16-19(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)北京市西城区2022-2023学年高二下学期期末考试数学试题
4 . 已知数列
:
,
,…,
,其中
是给定的正整数,且
.令
,
,
,
,
,
.这里,
表示括号中各数的最大值,
表示括号中各数的最小值.
(1)若数列
:2,0,2,1,-4,2,求
,
的值;
(2)若数列
是首项为1,公比为
的等比数列,且
,求
的值;
(3)若数列
是公差
的等差数列,数列
是数列
中所有项的一个排列,求
的所有可能值(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/f8f766fe39702fecd2b6c21855757907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33527f5f2178a3e7eb7df6cc0a676b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a146d1ac165f167e593bf6b03933e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0ce19d6ffec84ee7334568e933a95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d841396c105ff03a35898d4b96587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a146d1ac165f167e593bf6b03933e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fd8291ffa0740c3f6d0233cd3a5568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0b65265063085f628e232c2c2a8338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9626c69b9ef5db5e22540c404c4a6f.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30072a9cd1d03b6cf2c62c85df63d940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1724a17ff17abe389c4decf0b5e7bd8c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c8f394783e3687c602c7099cd420c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3012337aa392709349731fb1eef5b5.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/d92a355bfe012a120d10f677002922c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-05-06更新
|
1613次组卷
|
6卷引用:2022年新高考北京数学高考真题变式题13-15题
(已下线)2022年新高考北京数学高考真题变式题13-15题(已下线)重难点08 七种数列数学思想方法-1(已下线)2022年新高考北京数学高考真题变式题19-21题(已下线)北京市西城区2022届高三二模数学试题变式题16-21北京市西城区2022届高三二模数学试题北京市第九中学2022届高三下学期保温考试数学试题
名校
5 . 记实数
、
中较小者为
,例如
,
,对于无穷数列
,记
.若对任意
均有
,则称数列
为“趋向递增数列”.
(1)已知数列
、
的通项公式分别为
,
,判断数列
、
是否为“趋向递增数列”?并说明理由;
(2)已知首项为
,公比为
的等比数列
是“趋向递增数列”,求公比
的取值范围;
(3)若数列
满足
、
为正实数,且
,求证:数列
为“趋向递增数列”的必要非充分条件是
中没有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6323f3d42a8c329f1231a4183cca21c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d009da28dbbec2e0493e504b153d5e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467d1e5a0787b9a3d892291abc5216a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70642e7d9ccc8591908f12eea59c9daa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34916ec3b585a5926485d45191591e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](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/ccbb83894b8870017f24b5649ddc6360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4412c62615c55a6f09fcd4d54b10488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d42b37737d111c9e40136a4aa3266f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
您最近一年使用:0次
2022-11-06更新
|
1496次组卷
|
8卷引用:第10讲 数学归纳法与数列综合应用 - 1
(已下线)第10讲 数学归纳法与数列综合应用 - 1(已下线)专题06数列必考题型分类训练-3(已下线)专题1 数学归纳法及其变种 微点3 数学归纳法综合训练(已下线)模块九 数列-2(已下线)专题8 等比数列的单调性 微点1 判断等比数列单调性的方法(已下线)核心考点06数列-【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)上海市徐汇区2022届高三下学期二模数学试题上海市复旦大学附属中学2022-2023学年高二上学期期末数学试题
解题方法
6 . 已知函数
及其导函数
的定义域均为
.设
,曲线
在点
处的切线交
轴于点
.当
时,设曲线
在点
处的切线交
轴于点
.依此类推,称得到的数列
为函数
关于
的“
数列”.
(1)若
,
是函数
关于
的“
数列”,求
的值;
(2)若
,
是函数
关于
的“
数列”,记
,证明:
是等比数列,并求出其公比;
(3)若
,则对任意给定的非零实数
,是否存在
,使得函数
关于
的“
数列”
为周期数列?若存在,求出所有满足条件的
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3102c0a2f53b80f9dddbf9352537e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9df2062940530232ab124a571e951ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641fec779880f75fa8ee6782f3350402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c153922d3e1fec7dcb99c1713459547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f1a33d548a10c68b7eb6e170337975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27af938f6500dad80a84f808ec8012cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fe6d8eb256935b3cd0ffab906778d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aedadfc40b9928515b1db6045152643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c777afed064fe265ed8bcaee01521e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe8dc8e5def7d46b88535453ae1fd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2024-04-01更新
|
636次组卷
|
4卷引用:数学(上海卷02)
(已下线)数学(上海卷02)上海市浦东新区2024届高三下学期期中教学质量检测数学试卷(已下线)专题09 导数及其应用 压轴题(六大题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)广东省东莞中学、广州二中、惠州一中、深圳实验、珠海一中、中山纪念中学2024届高三下学期第五次六校联考数学试题
7 . 设
为实数,定义
生成数列
和其特征数列
如下:
(i)
;
(ii)
,其中
.
(1)直接写出
生成数列的前4项;
(2)判断以下三个命题的真假并说明理由;
①对任意实数
,都有
;
②对任意实数
,都有
;
③存在自然数
和正整数
,对任意自然数
,有
,其中
为常数.
(3)从一个无穷数列中抽出无穷多项,依原来的顺序组成一个新的无穷数列,若新数列是递增数列,则称之为原数列的一个无穷递增子列.求证:对任意正实数
生成数列
存在无穷递增子列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796bb39a2ab23cfdb6e463ab30a7af2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4758b555ca9b157cc074f1e4a092e34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f61c0bb2370087736c8e00e108b48c8.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c051dc675bcca6a8f70a3dbe922354.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3121951a9b059eef49b4a346d3aa2b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400b893304c51631873ded41027cf48.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e0c84de10f0f2186313169c3dc997b.png)
(2)判断以下三个命题的真假并说明理由;
①对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fbdf49cd00af1ff87259836ddd9f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508cd31480a898a71472e2d5d22377c7.png)
②对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fbdf49cd00af1ff87259836ddd9f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c99515d9952f2f7739fd750a31128f.png)
③存在自然数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a178f2c27906fc74afee1b7d7d52746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1563da7b0f046a469476668a3686e8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59a60eb4d63ebc879ae5c26413bcdcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)从一个无穷数列中抽出无穷多项,依原来的顺序组成一个新的无穷数列,若新数列是递增数列,则称之为原数列的一个无穷递增子列.求证:对任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da069077c220af26b9e77b02baeee4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4758b555ca9b157cc074f1e4a092e34a.png)
您最近一年使用:0次
解题方法
8 . 已知无穷数列
满足:①
;②
(
;
;
).设
为
所能取到的最大值,并记数列
.
(1)若
,写出一个符合条件的数列A的通项公式;
(2)若
,求
的值;
(3)若
,求数列
的前100项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6b7c794c3329ca99a71eb07c4a7b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8d9def91c6734e75134ef49ba0418a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a21caee5b908cd571bf28d61be90aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228114fab3c07bc63978df7e2dc31953.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8faa0cc59f291d53f801546d5dabe6fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa5e5f1551d40f96a03ca6975e68f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d00457e8d086f28ea1b24bd880c9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297bc58fc87efa1f15d7eb9b5eb42260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fb6fbf69268bc82274bc7ff03010c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51cf6e2a57173496d722a325ffd16af.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e35c9a35017d2fdcd10f76b4a776419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879ed18e2aaf5ef408be9e6ac8d9e30a.png)
您最近一年使用:0次
2022-05-30更新
|
1422次组卷
|
5卷引用:2022年新高考北京数学高考真题变式题13-15题
(已下线)2022年新高考北京数学高考真题变式题13-15题(已下线)2022年新高考北京数学高考真题变式题19-21题北京卷专题18数列(解答题)(已下线)专题11 数列前n项和的求法 微点8 分组法求和北京市东城区2022届高三下学期综合练习(三)数学试题
解题方法
9 . 定义:若数列
满足
,则称
为“Titus双指数迭代数列”.已知在“Titus双指数迭代数列”
中,首项
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c55dd214d8da6bb31d1d919dbe5628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412e419f8b8bf3ee0e1f68163cb1753c.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
您最近一年使用:0次
名校
10 . 设数列
.如果
,且当
时,
,则称数列A具有性质
.对于具有性质
的数列A,定义数列
,其中
.
(1)对
,写出所有具有性质
的数列A;
(2)对数列
,其中
,证明:存在具有性质
的数列A,使得
与
为同一个数列;
(3)对具有性质
的数列A,若
且数列
满足
,证明:这样的数列A有偶数个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65a1fd37e986a6657263d566fb2cb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f73d7a8c77f88995a3c89492b53b67de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4915d8f9706190d4d0b14aa42c2c7367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e2e9b1c158c5d4e2a1a2e1737013a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e8ef85162d03adbe3a2a6b7b19623.png)
(1)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fcf8639f59fb0ef4f9f6f6d0943a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57314e95aa54ed318c5fed57bc6d93fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1573d16b04edc29edf1340c9da13954c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40451e0f90ba4df0cb35143b93303a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(3)对具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e533e28452c0a087f29194aeb081523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40451e0f90ba4df0cb35143b93303a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0a22166c3eea2f12145d1906289a5a.png)
您最近一年使用:0次
2022-04-06更新
|
1366次组卷
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8卷引用:北京卷专题18数列(解答题)