1 . 设
.在
的方格表的每个小方格中填入区间
中的一个实数.设第
行的总和为
,第
列的总和为
,
.求
的最大值(答案用含
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f98da45d4de19a962cfa1d186e2755a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ace7d64e7ff100db25a07330654d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af908bca1b10f5de7e2d8979989c806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aba126d3f244b529547fa33b1dc5f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a71c7129333f890292aa75bc1d080a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023高三·全国·专题练习
解题方法
2 . 设无穷数列
满足
,
.证明∶
(1)当
时,
.
(2)不存在实数c,使得
对所有的n都成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbe9b03dd00928ca455cb9020c134f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1331e7312207f1a04187e4ae8dc9f54.png)
(2)不存在实数c,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6866e074b1f11e91aa70be5e367345ca.png)
您最近一年使用:0次
3 . 设
为整数.有穷数列
的各项均为正整数,其项数为m(
).若
满足如下两个性质,则称
为
数列:①
,且
;②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4daddea99be0888d1d6c560987c4bc2.png)
(1)若
为
数列,且
,求m;
(2)若
为
数列,求
的所有可能值;
(3)若对任意的
数列
,均有
,求d的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.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/280f1e7d3e287061e928c064f2197e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7577a0af23649b4a2a25326fb9499c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b02eaacb42cc64295856fefdd5d287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4daddea99be0888d1d6c560987c4bc2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c39770fd747beb3f0431bd6e86876e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43703b905a9846c8f49f23b07ca661d.png)
您最近一年使用:0次
2023-05-05更新
|
1848次组卷
|
6卷引用:北京卷专题18数列(解答题)
北京卷专题18数列(解答题)(已下线)专题15 数列不等式的证明 微点1 反证法证明数列不等式(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)北京市海淀区2023届高三二模数学试题北京市朝阳区2024届高三上学期数学期中模拟数学试题江苏省南京市南京外国语学校2024届高三下学期2月开学期初考试数学试题
名校
解题方法
4 . 已知等比数列
的公比为q(
),其所有项构成集合A,等差数列
的公差为d(
),其所有项构成集合B.令
,集合C中的所有元素按从小到大排列构成首项为1的数列
.
(1)若集合
,写出一组符合题意的数列
和
;
(2)若
,数列
为无穷数列,
,且数列
的前5项成公比为p的等比数列.当
时,求p的值;
(3)若数列
是首项为1的无穷数列,求证:“存在无穷数列
,使
”的充要条件是“d是正有理数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45482d31d1d7448c9f3922b4d2a55331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8f1df735a4480e538fd1d067fbd577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c0d25496e9b663eeb6bf77245d326e.png)
![](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/980995738642db660248799a63a7bc52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9abd3fde752b027a8d3ca8255295b8.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
您最近一年使用:0次
2023-04-25更新
|
1607次组卷
|
3卷引用:北京卷专题18数列(解答题)
5 . 对于向量
,若
,
,
三数互不相等,令向量
,其中
,
,
,
.
(1)当
时,试写出向量
;
(2)证明:对于任意的
,向量
中的三个数
,
,
至多有一个为0;
(3)若
,证明:存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681bacf0944746afc82249f50ffb9000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f74901036e0163ee8f9e88e1d952aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08320e6e96f872f1fcf6ad8096ebaa10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7accba7c6d73b12592f0874c69339d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843ff24183004a105ff0c73a1fac6a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe08794bdcc386a700cf75d9bb0a255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7455cd15ac74993fb312181398b4695f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f7f0bf96b369de82471d9f6b6821b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f8c1951e1335981548165f738e6d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5dba77896ed93d7c27df9d0b2c2154.png)
(2)证明:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61fbe58f038432c468241d2771fb85d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f4ddebf0e34a5c3e9232ae66709aa.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3d50b452aca40b6e77c2a37ff5bac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8ae325b1927be368df207ed6051707.png)
您最近一年使用:0次
2023-03-28更新
|
727次组卷
|
3卷引用:专题9 周期数列 微点2 周期数列的“脸谱”识别
6 . 已知
为正整数数列,满足
.记
.定义A的伴随数列
如下:
①
;
②
,其中
.
(1)若数列A:4,3,2,1,直接写出相应的伴随数列
;
(2)当
时,若
,求证:
;
(3)当
时,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97559b8ae5f9544c7b93bf2f9d03394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6559598727fb120a5cdbf4f15510615d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c995ba5a9caa036977b023f57a4202f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271c5044aeaf0fd2a6f75746754565c8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880b1efd3798a3ccf2633252b10e0ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570d7b5b193a644beb91889bbde27cde.png)
(1)若数列A:4,3,2,1,直接写出相应的伴随数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3053e2b8a6bbc35527a1e4505b84ed0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2578cb9428c41fa9236c6350bae49f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941e10d4febad08273c2b181023f019f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2578cb9428c41fa9236c6350bae49f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fac29b7c846a7ba3b612b0f7ebee41.png)
您最近一年使用:0次
2023-01-12更新
|
955次组卷
|
4卷引用:北京市西城区2022届高三二模数学试题变式题16-21
解题方法
7 . 已知数列
满足
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cae75fa078f0961c2966220d895b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92aa912f0e077e18b40bcb2d35de084.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)若
在区间
上单调递增,求a的取值范围;
(2)证明:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae48272779f294b8dd0b74ec94d0422.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1522e9d83de2b82983105a0fb3468f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83fd0c13ff68c422a80054b285ad6c0.png)
您最近一年使用:0次
2022-05-27更新
|
1338次组卷
|
3卷引用:专题15 导数综合
名校
9 . 已知集合
(
且
),
,且
.若对任意
,
,当
时,存在
,使得
,则称
是
的
元完美子集.
(1)判断下列集合是否是
的3元完美子集,并说明理由;
①
;
②
;
(2)若
是
的3元完美子集,求
的最小值;
(3)若
是
(
且
)的
元完美子集,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952f1e0ce5bd53a6d5e8bb07ea2da5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410a811a99d6f15164cdda4597323168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dd50a4fd2329323aa21597e8ff664b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e676073a8d2acb1678fdc705e33f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aadf01e5fac133cf390407bfad26b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d169a02afabbe304cf64b355bf71742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断下列集合是否是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49972f77c4c3b89116f02cbaba7f9089.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc21b9d3aa5f307d9c9d63ffaf68dc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfbdcd7014f79de428c1d5e6525aecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0604cb71df25c9b90c5d7521d3edd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8ab57234dfc54a5315381c59c94f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717995559c925685dacedc60be48fd03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf7c557b1aadac2ee7012fb1e1ba5f8.png)
您最近一年使用:0次
2022-05-12更新
|
738次组卷
|
4卷引用:专题16 数列新定义题的解法 微点2 数列新定义题综合训练
(已下线)专题16 数列新定义题的解法 微点2 数列新定义题综合训练北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题重庆市杨家坪中学2022-2023学年高一上学期10月月考数学试题北京市第二中学2022—2023学年高一下学期第六学段阶段性考试数学试题
10 . 已知数列
满足
,
,
为数列
的前n项和,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/8e80a50771f5f707926147a73de8f3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-04-23更新
|
1760次组卷
|
5卷引用:考点13 数列概念及通项公式(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)
(已下线)考点13 数列概念及通项公式(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)(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-1浙江省嘉兴市2022届高三下学期4月教学测试(二模)数学试题浙江省2022届高三下学期高考冲刺卷(二)数学试题浙江省嘉兴市嘉善中学2022届高三下学期5月适应性考试数学试题