23-24高一上·上海·期中
名校
1 . 对于正整数
,定义
.对于任意的
,称
为
的第
个分量,称
是
的一个“协同子集”.如果
同时满足:①
的元素个数不少于
;②对于任何
、
、
,存在
,使得
、
、
的第
个分量都是
.
(1)对于
,若
是
的一个恰好含有四个元素的“协同子集”,且其中两个元素是
和
,直接写出另外两个元素;
(2)证明:若
是
的一个“协同子集”,则
的元素个数不超过
;
(3)证明:若
是
的一个“协同子集”,且
的元素个数恰好是
,则存在唯一的
,使得
中所有元素的第
个分量都是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d3dc6cad699aa2713482c9f4306802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6aa5d5b774230400311326853ed898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a86c79fb771a07a413c755e4295b160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01433c50807a7878f60c05f43c3fa652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9154d05e636d76f2726e226a5ef3d7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b01af54049b27ca6e8159518b7b18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968b3f41b9a2f481de4b9d95547c5423.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e1f6f6f70deeead9aa004fe0697323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
名校
2 . 已知等差数列
的公差
,数列
满足
,集合
.
(1)若
,
,求集合
;
(2)若
,求
使得集合
恰有两个元素;
(3)若集合
恰有三个元素,
,T是不超过5的正整数,求T的所有可能值,并写出与之相应的一个等差数列
的通项公式及集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175e0a99f539fd0efcef57d600c69ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1969f7921af8e67d69baf43ef6dcaac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3699c6ebe26342584acf12920390bfe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c084b075abfacc73dc071c1d53ec01c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/197b1f83881a79aefe8db3f6dc7a8945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40af633ef92ee8b7889aed25d78549f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2019-08-16更新
|
677次组卷
|
3卷引用:上海市大同中学2018-2019学年高一下学期期中数学试题
上海市大同中学2018-2019学年高一下学期期中数学试题(已下线)上海期末真题精选50题(大题压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)河北省衡水市衡水中学2019-2020学年高三上学期期中数学(理)试题