1 . 我们称各项均不相等的正项数列
为“冒泡数列”,对任意冒泡数列,我们按如下步骤进行操作,称为“冒泡操作”
比较
的大小,若
,则交换
的位置;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,若
,再交换
;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,
,直到比较得到
时或者
调整位置至首位时停止比较和交换位置,并进行下一步;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,…,直到比较得到
或者
调整位置至首位时结束操作.
(1)请对数列
5,3,2,9,7作冒泡操作,可表示为
请写出操作结束后得到的数列,并计算交换位置的次数.
(2)对于某个
项冒泡数列
当其完成冒泡操作时的总的交换位置的次数称为其“交换复杂度”,记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a802b2e8db56dfb2f367fbbd9c4fe0f.png)
(i)求
的最小值和最大值;
(ii)对于某个
项冒泡数列
及其各项全排列产生的所有不同数列,其交换复杂度的平均数记为
,求
的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8e9680996fdd9e3a40f62d810e92e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa559d2ca921738d0c6c51f3a036880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ade3a1d01605706801e238726e55fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cfe1386cf3dae99d19bf57895c9f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a25a0b38f47e113fd4dd76832de690a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fee2a3f8c67509707271a3f266a8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8784badc8cc600bef381da22d1c628d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fee2a3f8c67509707271a3f266a8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0525db7ca68c21dfe7a1c4b543b4bee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9017d3641140e0692048ddbab24d1d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0525db7ca68c21dfe7a1c4b543b4bee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5356eacad97dae1c7e865903171245ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee15a08d7dc7c77ea81607b1f214c092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebefe3e26bef1c8422bfe5a472e0d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bc971d069730aa97e8734fc884e3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebefe3e26bef1c8422bfe5a472e0d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240e1ed0392e64705738776ff88b1623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0d398803d6a57b99fbb7994edc767b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed3a0a9f46932f86611d64711d81c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cace8ff9678eca7c3386f280c4ed8c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a67cfcf87e8b88246d7c8e101041bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0be03feff9bfb3b2f45a34b6fc2578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a67cfcf87e8b88246d7c8e101041bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d151f7e01f394c4547e8065de1adb689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5aeba46b164eea610a02251cdbfba03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)请对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569675dd7b2aca2732324f4bea5c02e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acd875285006bca9792d6ffbea60191.png)
(2)对于某个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be66b629b36c5fe55ff234ad59bffff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a802b2e8db56dfb2f367fbbd9c4fe0f.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94511620a0ee01ebcc8ac2f3a47ac87d.png)
(ii)对于某个
![](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/de53713b20a2f956c2590ce71fb69c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de53713b20a2f956c2590ce71fb69c37.png)
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名校
2 . 已知数列
的通项为
,前
项和为
,则下列选项中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.如果![]() ![]() ![]() ![]() |
B.如果![]() ![]() ![]() ![]() |
C.如果![]() ![]() ![]() ![]() |
D.如果![]() ![]() ![]() ![]() ![]() ![]() |
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3卷引用:湖南省长沙市第一中学2024届高三下学期模拟试卷(二)数学试题
3 . 若数列
在某项之后的所有项均为一常数,则称
是“最终常数列”.已知对任意
,函数
和数列
满足
.
(1)当
时,证明:
是“最终常数列”;
(2)设数列
满足
,对任意正整数
.若方程
无实根,证明:
不是“最终常数列”的充要条件是:对任意正整数
,
;
(3)若
不是“最终常数列”,求
的取值范围.
![](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/4bc6de641322c6aeb24e0bbd875e65b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980f4d5c5ec0f551d7a3c3c0b5ffdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b26218ecae19cc13017d561c01d69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36737370e7f4231ebdd27c957f47f45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8f2cc86844dc647bfb33344781e75a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c77ea288be5bfb4445a76a2429aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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名校
4 . 超越数得名于欧拉,它的存在是法国数学家刘维尔(Joseph Liouville)最早证明的.一个超越数不是任何一个如下形式的整系数多项式方程的根:
(
,
,…,
,
).数学家证明了自然对数的底数e与圆周率
是超越数.回答下列问题:
已知函数
(
)只有一个正零点.
(1)求数列
的通项公式;
(2)(ⅰ)构造整系数方程
,证明:若
,则
为有理数当且仅当
.
(ⅱ)数列
中是否存在不同的三项构成等比数列?若存在,求出这三项的值;否则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc2287a601b334908c58609a5ce2f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf1336dd233a8630e7266f0a83dea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b3c450d9e72a71e5d2562c48e7cb6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)(ⅰ)构造整系数方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1641897cacc61faed30907970d1fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5dd1562138ab60802c33a17a8d7867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d835c32139c51bc210b9714048fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
(ⅱ)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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2卷引用:湖南省部分学校2024届高三下学期一起考大联考模拟(二)数学试题
5 . 设整数
满足
,集合
.从
中选取
个不同的元素并取它们的乘积,这样的乘积有
个,设它们的和为
.例如
.
(1)若
,求
;
(2)记
.求
和
的整式表达式;
(3)用含
,
的式子来表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c4b8f96da2495ecc059119eb01e0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7601dbefa6836756e3d2731b79af0126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8086c293be0cdc3a19d585bbe148da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdea830c734212c9831f428918636e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfd4e75e49d369dcc3e961c6b58eafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34dac6973b2d824ea18182ebaac82284.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d7245bd8cc47b87eeb270d4f39ee4b.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55746d3923c7cf11339076311286165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f5dcdd63776d5b10d1e5612abdaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065724f62f61254af999bb5a7c9beb95.png)
(3)用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86582734340e1b08498b0645d85a55b.png)
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3卷引用:湖南省衡阳市第八中学2024届高三下学期高考适应性练习数学试卷
名校
解题方法
6 . 基本不等式可以推广到一般的情形:对于
个正数
,它们的算术平均不小于它们的几何平均,即
,当且仅当
时,等号成立.若无穷正项数列
同时满足下列两个性质:①
;②
为单调数列,则称数列
具有性质
.
(1)若
,求数列
的最小项;
(2)若
,记
,判断数列
是否具有性质
,并说明理由;
(3)若
,求证:数列
具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efff8ec14cb242e793afab4468bf2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2617515e5ce81b3f5d9f4e806b21b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6879960be91ea52297d587e9a014f54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce59ae5baacab766b0915722377a746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bc99b9545c8c838e99b7be9c6d1046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20e03ee7d9307a0a4d242fffda381d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247739746b8ddf1403541047e8b5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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|
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7卷引用:湖南省2024年高三数学新改革提高训练三(九省联考题型)
湖南省2024年高三数学新改革提高训练三(九省联考题型)安徽省部分省示范高中2024届高三开学联考数学试卷湖北省荆州市沙市中学2024届高三下学期3月月考数学试题(已下线)黄金卷04(2024新题型)广东省广州市西关外国语学校2023-2024学年高二下学期期中数学试题(已下线)压轴题03不等式压轴题13题型汇总-2辽宁省朝阳市建平县实验中学2024届高三第五次模拟考试数学试题
22-23高三下·北京海淀·开学考试
名校
解题方法
7 . 若无穷数列
的各项均为整数.且对于
,
,都存在
,使得
,则称数列
满足性质P.
(1)判断下列数列是否满足性质P,并说明理由.
①
,
,2,3,…;
②
,
,2,3,….
(2)若数列
满足性质P,且
,求证:集合
为无限集;
(3)若周期数列
满足性质P,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9672f1800f9544e878955f289aa3fc6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f2c7c9305b404f7363a376af101aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa38a89b95fa1ea7bfc91630f6c7437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0fbad04faddb5408ce4e7e6e3ed816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)判断下列数列是否满足性质P,并说明理由.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ce6401cf48b9546342b1b96ac2cc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
(2)若数列
![](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/f224a5a66c91792eceb8f8c725183f67.png)
(3)若周期数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2024-02-10更新
|
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14卷引用:湖南省2024届高三数学新改革提高训练一(九省联考题型)
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解题方法
8 . 已知数列
为有穷正整数数列.若数列A满足如下两个性质,则称数列A为m的k减数列:
①
;
②对于
,使得
的正整数对
有k个.
(1)写出所有4的1减数列;
(2)若存在m的6减数列,证明:
;
(3)若存在2024的k减数列,求k的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed25314606b875ae6cdfa2d073c73c85.png)
②对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ae1214cc78e72fb613d7e649bc27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b3392579424244c50ddf416ee3434d.png)
(1)写出所有4的1减数列;
(2)若存在m的6减数列,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409ce4e6aa8638fe5880009dbb732f7.png)
(3)若存在2024的k减数列,求k的最大值.
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2024-01-25更新
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9卷引用:湖南省长沙市雅礼中学2024届高三下学期数学月考试卷(八)
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9 . 已知无穷数列
,
.性质
,
,;性质
,
,
,下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61afe83270a244e2af1995c9f4f51f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8af17844e7059b9c96c75c8440671eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5a0c2ef759ad38721f51ad2298c66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0971a0dad04b09fab7c3f0eafe5b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e7bd4fde43499209812ba20f87286c.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若等比数列![]() ![]() |
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3卷引用:湖南省衡阳市第八中学2024届高三下学期高考适应性练习(一)数学试题
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10 . 设
为给定的正奇数,定义无穷数列
:
若
是数列
中的项,则记作
.
(1)若数列
的前6项各不相同,写出
的最小值及此时数列的前6项;
(2)求证:集合
是空集;
(3)记集合
正奇数
,求集合
.(若
为任意的正奇数,求所有数列
的相同元素构成的集合
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77576292d833c93bdcf4da9787ee0db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003dd0feaa12a01db4c777784889c374.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3884cadaff5a78756698d57c41f305d.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611448a63d973f73f8c0026dd38ac932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7dbf7c1220f9db7d313570143f4a709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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4卷引用:湖南省2024届高三数学新改革提高训练二(九省联考题型)
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