名校
1 . 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)
您最近一年使用:0次
2 . 若数列
和
的项数均为
,则将数列
和
的距离定义为
.
(1)求数列1,3,5,6和数列2,3,10,7的距离;
(2)记A为满足递推关系
的所有数列
的集合,数列
和
为A中的两个元素,且项数均为
.若
,
,数列
和
的距离
,求m的最大值;
(3)记S是所有7项数列
(其中
,
或1)的集合,
,且T中的任何两个元素的距离大于或等于3.求证:T中的元素个数小于或等于16.
![](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/294f5ba74cdf695fc9a8a8e52f421328.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/58eb2bc16ca7ba6db8792eec6e2b48c0.png)
(1)求数列1,3,5,6和数列2,3,10,7的距离;
(2)记A为满足递推关系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23093a3f4c23494a943e3957596fee92.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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2865594c03cd3cfcbf3216cdbf08fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cb4aa359781e637bd2232813fa8a24.png)
(3)记S是所有7项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d7457bc36b80660dc03b668674f065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c458592ba2d5ddd559b8720438a8fe.png)
您最近一年使用:0次
3 . 对于数列
,
,…,
,记
,
.设数列
,
,…,
和数列
,
,…,
是两个递增数列,若A与
满足
,
,且
,
,则称A,
具有
关系.
(1)若数列A:4,7,13和数列
:3,
,
具有
关系,求
,
的值;
(2)证明:当
时,存在无数对具有
关系的数列;
(3)当
时,直接写出一对具有
关系的数列
和
.(本小问不用写解答过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b371f2c03f281c6b3a8d177c99396e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fccdb5805293481f533355378857a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ea8a3bb7046d6cd460fcf8eeaa9572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140b9dbcada4ac2e5fe3cc30009bcd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17923637012a75a01f309379c1909c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8f57cd414df79b3a3f914a970e3844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66b99e1ab7bcbc27f97648a865d69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dfd2f6a994a79d0d3ebd56ecb4f3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757098572cb879ed0681a73db908af74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ce2f8d8c7e266a9fb318a8d3bcd404.png)
(1)若数列A:4,7,13和数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ce2f8d8c7e266a9fb318a8d3bcd404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ce2f8d8c7e266a9fb318a8d3bcd404.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ce2f8d8c7e266a9fb318a8d3bcd404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
4 . 设数列
的前
项和为
.若对任意的正整数
,总存在正整数
,使得
,则称
是“
数列”.
(1)若
,判断数列
是否是“
数列”;
(2)设
是等差数列,其首项
,公差
,且
是“
数列”,
①求
的值;
②设
为数列
的前
项和,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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3693c7c942afef5517a3c18997c878df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10528a2f11fe3d860307b076906aaa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6870c5f54b5f42164c349f150f0b724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b9a7705275fa6679eb106d6b77c7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b93c0a7a990bfd7c5b0af6cbc0f02b.png)
您最近一年使用:0次
名校
解题方法
5 . 数列
中,从第二项起,每一项与其前一项的差组成的数列
称为
的一阶差数列,记为
,依此类推,
的一阶差数列称为
的二阶差数列,记为
,….如果一个数列
的p阶差数列
是等比数列,则称数列
为p阶等比数列
.
(1)已知数列
满足
,
.
(ⅰ)求
,
,
;
(ⅱ)证明:
是一阶等比数列;
(2)已知数列
为二阶等比数列,其前5项分别为
,求
及满足
为整数的所有n值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c599a8303d934678c8cae0ed864b776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c599a8303d934678c8cae0ed864b776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5452a758da0f722da03128a5eb3ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f88267cbc5e8e016b1a92bcf0fb27d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281cde49dcc279bdc6b2a99edafe19da.png)
(1)已知数列
![](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/3998df04d0a8ded946c3f39d545fdc7e.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f94c7bb2d2afc4196b15f6879ddf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e9e4a01bdaa1f768225e055b6c6d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13df1f8f074ab49fc065ed0da2d5aff.png)
(ⅱ)证明:
![](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/0965cc6a58c25d9ba7876da319a8cae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
2024-05-07更新
|
922次组卷
|
3卷引用:北京市中国人民大学附属中学2023-2024学年高二下学期统练3数学试题
名校
6 . 给定正整数
,若项数为
的正实数数列
满足:
,且
,称数列
为“
数列”.如果“
数列”
存在
分别是一个锐角三角形的三个边长,则称这个
项数列
为“
数列”.
(1)判断数列
:2,2,2,2,2和数列
:1,2,3,4,5是否为“
数列”;
(2)正数数列
满足:
.证明:数列
是“
数列”,但不是“
数列”;
(3)若任意的
项“
数列”
均为“
数列”,求出所有满足条件的整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527093b2ec760913d0dccff8a099248b.png)
![](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/f21260db76bccbe864f3ca0a2a73560d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4336bcbdedc39981ecb5b341d3a72696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6a7df080c1d6de0e9c0b4fe5234ff3.png)
![](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/9b1ec05e3cec27677ded7b4aecaa62d3.png)
(1)判断数列
![](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/9b1ec05e3cec27677ded7b4aecaa62d3.png)
(2)正数数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4574c36c387499c27d69e20b689b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
(3)若任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
7 . 若实数列
满足
,有
,称数列
为“
数列”.
(1)判断
是否为“
数列”,并说明理由;
(2)若数列
为“
数列”,证明:对于任意正整数
,且
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97bb4c969108ebef4ebadd5acc5ca4.png)
(3)已知数列
为“
数列”,且
.令
,其中
表示
中的较大者.证明:
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fee3639b8e3ff9717f3ffd9633927f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8414472e2121e1796eb40408d820053a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f1bc95528c774ce919f7c5a0ef0d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d7e68d0c8bd9a32d826c721ab74d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e517c32ed93de4d9cb6e0926337000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97bb4c969108ebef4ebadd5acc5ca4.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93846b72089bd425864969f2edabdb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8957564d30af14db69fdc36be2eaee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065f8a641aab5c39f73be89a6f2e7a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4dc7e8bd20e9d38b4d248a8c253ccd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8131eb05d480f0da6c61ebda3ce48.png)
您最近一年使用:0次
名校
解题方法
8 . 对于有穷数列
,若存在等差数列
,使得
,则称数列
是一个长为
的“弱等差数列”.
(1)证明:数列
是“弱等差数列”;
(2)设函数
,
在
内的全部极值点按从小到大的顺序排列为
,证明:
是“弱等差数列”;
(3)证明:存在长为2024的“弱等差数列”
,且
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce381e1cb026a858d8c7b94e1754844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43a56a30994f7d7e2f15da593b05a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a56586686dfb815fe548957ddcfefb.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1947fd8b1e5fa9096c13256fdb3a23ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7833e32ccdb51745b01fc7877762492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
(3)证明:存在长为2024的“弱等差数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
9 . 已知各项均不为0的数列
满足
(
是正整数),
,定义函数
,
是自然对数的底数.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)记函数
,其中
.
(i)证明:对任意
,
;
(ii)数列
满足
,设
为数列
的前
项和.数列
的极限的严格定义为:若存在一个常数
,使得对任意给定的正实数
(不论它多么小),总存在正整数m满足:当
时,恒有
成立,则称
为数列
的极限.试根据以上定义求出数列
的极限
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bf7b5dc247fe10b6bfd984413a5e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd9ea8ffdea8c77370ea3e5f563dc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fec2729d8e927de9392ee90d1e0389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6f0a55fa53bf5f8e6654897975bcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3324481138f2dc750f9ad889054abe1.png)
(i)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416a72de4d0030203a867cc3b7b95d83.png)
(ii)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0857559ed421cc7c614708f34f9f3324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9de1835c164233db8b623489fbda0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
10 . 已知数列
的各项均为正整数,设集合
,
,记
的元素个数为
.
(1)若数列A:1,3,5,7,求集合
,并写出
的值;
(2)若
是递减数列,求证:“
”的充要条件是“
为等差数列”;
(3)已知数列
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f885247785940c5c849210fb6f8abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4884c506476f191d7919cd266c8c0212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a0c2bb484bf523189b093485eca999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(1)若数列A:1,3,5,7,求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3197c615558fee3993d2a8deb9091f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d509697c5391a7c24d9bbc2c82422b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff241fc46c23ac975c5b39e87a9e46a.png)
您最近一年使用:0次
2024-04-19更新
|
318次组卷
|
3卷引用:吉林省长春市长春吉大附中实验学校2023-2024学年高二下学期5月期中考试数学试卷
吉林省长春市长春吉大附中实验学校2023-2024学年高二下学期5月期中考试数学试卷黑龙江省双鸭山市友谊县高级中学2024届高三下学期高考模拟(一)数学试题(已下线)2024年北京高考数学真题平行卷(基础)