名校
1 . 已知数集
具有性质
:对任意
,
与
两数中至少有一个属于
.
(1)分别判断数集
与
是否具有性质
;
(2)求证:
;
(3)给定正整数
,求证:
,
,
,
组成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7cdd844688e7a1b08f8ed3792760a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcdd8c05cd04f46c6f4ba8aa3cb1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c981868188750ab216366b8272d4b35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4489d9b83072184c0e1d6b09be50ca.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd14cb27cbdb43c432f7493c34575c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ec8506f11fb704c94772de34e05381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcdd8c05cd04f46c6f4ba8aa3cb1d0.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e6fc2c0740f9ff797037bcd1409768.png)
(3)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fee7283a714563ad255f3ef9ac1a30.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/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
2023-12-20更新
|
404次组卷
|
4卷引用:北京市海淀区中央民族大学附中2024届高三上学期12月月考数学试题
北京市海淀区中央民族大学附中2024届高三上学期12月月考数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编北京市北京师范大学燕化附属中学2023-2024学年高二下学期期中考试数学试卷
2 . 定义1:通常我们把一个以集合作为元素的集合称为族(collection).
定义2:集合
上的一个拓扑(topology)乃是
的子集为元素的一个族
,它满足以下条件:(1)
和
在
中;(2)
的任意子集的元素的并在
中;(3)
的任意有限子集的元素的交在
中.
(1)族
,族
,判断族
与族
是否为集合
的拓扑;
(2)设有限集
为全集
(i)证明:
;
(ii)族
为集合
上的一个拓扑,证明:由族
所有元素的补集构成的族
为集合
上的一个拓扑.
定义2:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)族
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee5abf02995c6ac2135347a663cdb0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92ee8109b0f949f8946814f0a69e8b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)设有限集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a75d83dc31194727f441b79eee9cfc.png)
(ii)族
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9350d17e3ce2d85030a0076b53174a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
名校
解题方法
3 . 设集合
,如果对于
的每一个含有
个元素的子集P,P中必有4个元素的和等于
,称正整数
为集合
的一个“相关数”.
(1)当
时,判断5和6是否为集合
的“相关数”,说明理由;
(2)若
为集合
的“相关数”,证明:
;
(3)给定正整数
,求集合
的“相关数”m的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfaf890572dd4d18e052c7f1b710a42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebb4fc3cab7c95de0b0729d3a67eff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41505e5e2ee8177abc71e367a0f9d53e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f762938f5c78eb72bafbb13bf85cba1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384e115ed1afd6a5ad426c966f639b52.png)
(3)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
您最近一年使用:0次
2023-08-27更新
|
562次组卷
|
6卷引用:北京市西城区2017届高三二模数学理科试题
北京市西城区2017届高三二模数学理科试题北京市西城区2017届高三5月模拟测试(二模)数学理试卷北京市景山学校2022届高三上学期期中考试数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)专题01 集合及集合运算求参(2)(已下线)专题01 集合及集合运算求参(2)-【寒假分层作业】(人教A版2019必修第一册)
名校
4 . 对于数集
(
为给定的正整数),其中
,如果对任意
,都存在
,使得
,则称
具有性质
.
(1)若
,且集合
具有性质
,求
的值;
(2)若
具有性质
,求证:
;且若
成立,则
;
(3)若
具有性质
,且
为常数,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4622c700325a90d453e6300b886a8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bc1a0bba5e6e8ddf6f1f60f78e6490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887982e3735dd7ca13293338a12df593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6dbbefb5a9955cdbe090c5f0b8a8d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cbab5722e0fb2df79a07cfe8f1164b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7511e6ce72a5232820b7007f976be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864dd49f786346bc320deace92f949b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551ee6e86b2c6e79236dfe3e2e2c24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346549f9adda7eb363f16d355ae68b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cf27bef9cafda3dd897e29f3fe1df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
元正整数集合
满足:
,且对任意
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e81d3dacb5e2e527b8daebcf19fc9.png)
(1)若
,写出所有满足条件的集合
;
(2)若
恰有
个正约数,求证:
;
(3)求证:对任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5fcfc55b56f04ac530871067e5ce71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5ba5a3d48da1d7f3952c013a5ee0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139ae1c18e2cded6d04808a3aa24c6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c7cb34e9b5c1ecd75ff1966e882ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e81d3dacb5e2e527b8daebcf19fc9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7979eac1b85b681ba94bf8d833c5c6e7.png)
(3)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa673986cef1873a421a572abf9ed71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cee7a77f2f4592cb5c96245ff025f8.png)
您最近一年使用:0次
名校
解题方法
6 . 设A是正整数集的一个非空子集,如果对于任意
,都有
或
,则称A为自邻集.记集合
的所有子集中的自邻集的个数为
.
(1)直接写出
的所有自邻集;
(2)若
为偶数且
,求证:
的所有含5个元素的子集中,自邻集的个数是偶数;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417abc71b8bee465746db0a35e776f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca2371b88985463ba25e4ec1ea453d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377240e8ad277805e0499803d5be5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623eef12f37f0b85ddd367faa9b3bfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aba3402e1d191ff96adda7c4af70ef.png)
您最近一年使用:0次
2023-05-28更新
|
706次组卷
|
11卷引用:北京市西城区2021届高三5月二模数学试题
北京市西城区2021届高三5月二模数学试题北京一零一中学2023届高三下学期数学统练四试题北京卷专题02集合(解答题)北京市第一0一中学2022-2023学年高三下学期统练数学试卷(四)北京市东城区景山学校2024届高三上学期12月月考数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)北京市第五十七中学2021-2022学年高二上学期期中检测数学试题北京市第二十中学2022-2023学年高二上学期12月月考数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列北京市北京师范大学第二附属中学2023-2024学年高二上学期期中测试数学试题北京市第二中学2023-2024学年高二上学期12月第二学段考试数学试卷
7 . 在
)个实数组成的n行n列的数表中,
表示第i行第j列的数,记
,
若
∈
,且
两两不等,则称此表为“n阶H表”,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
且
,求证:
为偶数;
(3)求证:不存在“5阶H表”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff6f8857124f7bbc5a1c65c2e83767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c9ff2b00c2841318b2697b070201a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2fe368efe94c1e98309473e49a92fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d253e22a1d9709dca48c6e0c649b47bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0fdc4f349ea9634160ce08ac269691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db8c7f00e535ec1ffbb7008711b2096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8810a8ced3ca8dae09180a663275b425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)求证:不存在“5阶H表”.
您最近一年使用:0次
2023-03-14更新
|
865次组卷
|
5卷引用:北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题
北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题北京市第一0一中学2023届高三数学统练三试题北京市第十一中学2023届高三三模(5月)数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)微考点8-1 新高考新题型19题新定义题型精选
名校
解题方法
8 . 已知数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f155247fc662b89c545ea34094b778d6.png)
,
,…,
的各项均为正整数.设集合,
记
的元素个数为
.
(1)若数列
1,1,3,2,求集合
,并写出
的值;
(2)若
是递增数列,求证:“
”的充要条件是“
为等差数列”;
(3)若
,数列
由1,2,3,…,11,22这12个数组成,且这12个数在数列
中每个至少出现一次,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f155247fc662b89c545ea34094b778d6.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/8d8e6e9e456eb7ed9de302990075d1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3093d1159a994b153db26d1ba23c567f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f155247fc662b89c545ea34094b778d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be63af01fc637c108801b34882acc1a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807511534842b45a837c0fe12754345e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
您最近一年使用:0次
9 . 正整数集合
,且
,
,
中所有元素和为
,集合
.
(1)若
,请直接写出集合
;
(2)若集合
中有且只有两个元素,求证“
为等差数列”的充分必要条件是“集合
中有
个元素”;
(3)若
,求
的最小值,以及当
取最小值时,
最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59003c6febf1a45fc85bc475a3a17b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c002c44d45907aad22da19859193270b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd8ff87ff3fef45414f594ae017351e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bef20fc87980ef78c7f8eebd15f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d02a8555da4dbbc7820a50a95b071ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629455b181f187fe9b0edd9d66431ef0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143d9d0954abea7adb3412216fe8daf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
10 . 数列
的前n项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
组成集合
,从集合
中任取
个数,其所有可能的k个数的乘积的和为
(若只取一个数,规定乘积为此数本身),例如:对于数列
,当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca6aed34ac7a9ec7a2c99017258950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2a2e79473c0dae68bbfc032eb5d374.png)
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d0f03653307d27a5d3cf0651ae59c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65124bfe2a0b72ab2a5ce2699e96ea40.png)
;
(1)若集合
,求当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c841708c1ad65be3b5d71fa2bfad2698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0f2a2edfeb8e72c6b31925418cef55.png)
的值;
(2)若集合
,证明:
时集合
的
与
时集合
的
(为了以示区别,用
表示)有关系式
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79625fa88ed03a4ab346113c1b74ee08.png)
;
(3)对于(2)中集合
.定义
,求
(用n表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e07bf129b073f37b553fbca100172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929d4439a3528ff0dbda8a4c15e50684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51342bd3cf34520879288321fff9e995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a996c4e29bcc381353e072eb04c11b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000878a4785933077d2047002ceefe64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca6aed34ac7a9ec7a2c99017258950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2a2e79473c0dae68bbfc032eb5d374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d0f03653307d27a5d3cf0651ae59c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65124bfe2a0b72ab2a5ce2699e96ea40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ed17c0a08822cec43834a328a9459a.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7e83978c34e6eb0949e09efbb32e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c841708c1ad65be3b5d71fa2bfad2698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0f2a2edfeb8e72c6b31925418cef55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c5f3a5c55e0c95191c5a893f63062.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2cb003e606c759ff3c11589dacb5d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e74be91bfe4bc209da7539dbf9b72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e2eab067846bbece47c58b5f172214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e74be91bfe4bc209da7539dbf9b72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3452989a9088b492a453b9bcadb4d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef55dcc5a8256029a4e421325fb0a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79625fa88ed03a4ab346113c1b74ee08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff8f43f54aaab94d126c2ed7c929196.png)
(3)对于(2)中集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22d7376f2a56d0059105bc63ed7c4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-05-23更新
|
538次组卷
|
4卷引用:2017届上海市浦东新区高考三模数学试题
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