名校
1 . 设
,若其元素满足
,则称集合
为集合
的“
元封闭集”.
(1)写出实数集
的一个“二元封闭集”;
(2)证明:正整数集
上不存在“二元封闭集”;
(3)求出正整数集
上的所有“三元封闭集”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ca644ffc0b79661caf6ba7188ccc3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa9ca1afc43a859586c222be8064af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)写出实数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)证明:正整数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
(3)求出正整数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
您最近一年使用:0次
名校
2 . 数字
的任意一个排列记作
,设
为所有这样的排列构成的集合.集合
任意整数
都有
,集合
任意整数
都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9d89f2b4a2e160458b36c8fd270c89.png)
(1)用列举法表示集合
;
(2)求集合
的元素个数;
(3)记集合
的元素个数为
,证明:数列
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1862403f59a94ecf2d21fe7e19d2aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c686124767ab3c2b84470b065fcef89b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7bc57de21efd7fa1776a01591d99a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12df2ae8d3e915feafa1c5c21f2926e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767965df8401842b4d727998d43a4fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280a824d01ca8de7247b6e2ddd6fffdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e2febfa043de68251b23704c5e420a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9d89f2b4a2e160458b36c8fd270c89.png)
(1)用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f266dacf74b0a86d671a5a422f848cb9.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c612f58462180705a1acfd433714a4.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2020-04-03更新
|
712次组卷
|
4卷引用:2020届北京市清华大学附属中学朝阳学校高三第一学期第二次质量检测数学试题
名校
3 . 称正整数集合 A={a1,a2,…,an}(1≤a1<a2<…<an,n≥2)具有性质 P:如果对任意的i,j(1≤i≤j≤n),
与
两数中至少有一个属于A.
(1)分别判断集合{1,3,6}与{1,3,4,12}是否具有性质 P;
(2)设正整数集合 A={a1,a2,…,an}(1≤a1<a2<…<an,n≥2)具有性质 P.证明:对任意1≤i≤n(i∈N*),ai都是an的因数;
(3)求an=30时n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f52783e7a39f438adf08ef7d05d8c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf9fc9e8c9940547678ff7934363f52.png)
(1)分别判断集合{1,3,6}与{1,3,4,12}是否具有性质 P;
(2)设正整数集合 A={a1,a2,…,an}(1≤a1<a2<…<an,n≥2)具有性质 P.证明:对任意1≤i≤n(i∈N*),ai都是an的因数;
(3)求an=30时n的最大值.
您最近一年使用:0次
2020-01-31更新
|
361次组卷
|
4卷引用:上海市建平中学2019-2020学年高一上学期9月月考数学试题
上海市建平中学2019-2020学年高一上学期9月月考数学试题上海市建平中学2015-2016学年高一上学期期中数学试题沪教版(2020) 必修第一册 单元训练 期末测试(B卷)(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列
名校
4 . 对于集合
,定义函数
对于两个集合
,
,定义运算
.
(1)若
,
,写出
与
的值,并求出
;
(2)证明:
;
(3)证明:
运算具有交换律和结合律,即
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6897439ed76144996f77405e800fd67b.png)
对于两个集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e7e34beaff39ac5d8f3c7898804380.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbefb4190e6d31cf43ce5258ebf325c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc97700060520fb568f5aca7256b193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cea70b4969a5494ceb845f1818c26b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c55c7b14727415d05ed3557918ac38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5231cb0bfedf2f963c1830adfd74aa.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859bd72898c667a3e4c6976b6dcb020e.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7d51315fcca519cb58bacd0040d7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b4388c3b893c55b81e2b15ec4fa9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccff813e57fa8b0fb3649da671dc52b.png)
您最近一年使用:0次
2020-01-19更新
|
356次组卷
|
3卷引用:北京市日坛中学2023-2024学年高一上学期12月月考数学试题
名校
5 . 已知
是满足下列条件的集合:①
,
;② 若
,则
;③ 若
且
,则
.
(1)判断
是否正确,说明理由;
(2)证明:“
”是“
”的充分条件;
(3)证明:若
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca05074e5a317ae45d073962bdf74dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fefe237385a2dc1b005d8dc61ef56eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c443466385f21cd3f06e2e4229add79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ac8248bb70f9ef5b0cb7d025e05160.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de68508dc0a95fc4b5de772390260db.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79d04bf7882fd278b9ba53b791c156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f06a4a9deb51418c20e7e7376cc807.png)
您最近一年使用:0次
6 . 已知数集
具有性质
:对任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
、
,
,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
,并说明理由;
(2)证明:
,且
;
(3)当
时,若
,求集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef22ef7bcf6fffae9881d8b9b1b11ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601b3e081be3f86db147b0632622974a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dff86236cbe7f2a517f7f656d0afa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c751bc0dac0dba8d49f3429f55912d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f02bdffbaff7975c1c74162a1cb76a5.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2019-11-13更新
|
802次组卷
|
5卷引用:上海市向明中学2019-2020学年高一上学期9月质量监控考数学试题
名校
解题方法
7 . 给定整数
(
),设集合
,记集合
.
(1)若
,求集合
;
(2)若
构成以
为首项,
(
)为公差的等差数列,求证:集合
中的元素个数为
;
(3)若
构成以
为首项,
为公比的等比数列,求集合
中元素的个数及所有元素之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54d41b965c7b1771c84fabb87ae6258.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f77cadcea108fc0b1f680a8840a274c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2019-02-01更新
|
577次组卷
|
6卷引用:上海市七宝中学2020届高三上学期11月月考数学试题
上海市七宝中学2020届高三上学期11月月考数学试题北京市密云区第二中学2024届高三上学期10月月考数学试题上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题上海市曹杨二中2019-2020学年高二上学期期末数学试题北京市东城区景山学校2021届高三上学期期中数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21
名校
解题方法
8 . 设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4d1249a24300ebfc3d0219f5bb4d06.png)
是由
组成的
行
列的数表(每个数恰好出现一次),
且
.若存在
,
,使得
既是第
行中的最大值,也是第
列中的最小值,则称数表
为一个“
数表”
为数表
的一个“
值”,对任意给定的
,所有“
数表”构成的集合记作
.
(1)判断下列数表是否是“
数表”.若是,写出它的一个“
值”;
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9578b9d3e9f25d56b3cff92c362b7b9a.png)
(2)求证:若数表
是“
数表”,则
的“
值”是唯一的;
(3)在
中随机选取一个数表
,记
的“
值”为
,求
的数学期望
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4d1249a24300ebfc3d0219f5bb4d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0855b859cea85c928dceeb703492eec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ffc57987e8ce6bd4e034d3fa0d8b50.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/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1505d56f0b35fe7f2de1fe1888036e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f01cfc245e926581bdb125e0fba733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00d8f90655e6341907aa9c7c62d4398.png)
(1)判断下列数表是否是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7472089f40e32910ce97be398e3f2948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9578b9d3e9f25d56b3cff92c362b7b9a.png)
(2)求证:若数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2374064abe447ef286f69df90397abe.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/6b9e05eb5996d4c94049f6f5fa7d16e8.png)
![](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/9fc79c66ebaacd709ec9965b90a22b14.png)
您最近一年使用:0次
2018-04-14更新
|
612次组卷
|
2卷引用:北京市东城区广渠门中学2024届高三上学期12月月考数学试题
名校
9 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bc24b06e0abd218044a27f597fa9e5.png)
.对于
,
,定义
与
之间的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a724e5071732f90d91d468389e8e956a.png)
.
(1)写出
中的所有元素,并求两元素间的距离的最大值;
(2)若集合
满足:
,且任意两元素间的距离均为2,求集合
中元素个数的最大值并写出此时的集合
;
(3)设集合
,
中有
个元素,记
中所有两元素间的距离的平均值为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bc24b06e0abd218044a27f597fa9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855ce769f6795d1463744a0d74901fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f0f12e1350ca9c2a81b6c36a840365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bd6eccfd88084fd4b0c89c4c709d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a724e5071732f90d91d468389e8e956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3244bd0e909db80eb9e3ea79303b8351.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b626a2cad742c6613dc283fdab1e833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d7fa8a17135961c9c582f11d2e16cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1071ac8657ef1c4e1ea7e0530196298d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423cc16756424271a003917fbca775b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b67a5d723be5756086feeff090fe693.png)
您最近一年使用:0次
2017-04-06更新
|
962次组卷
|
2卷引用:北京市第八十中学2022届高三上学期10月月考数学试题
10 . 已知
,
或1,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6227cce99354c34b73c9e49a286348d.png)
,对于
,
表示U和V中相对应的元素不同的个数.
(Ⅰ)令
,存在m个
,使得
,写出m的值;
(Ⅱ)令
,若
,求证:
;
(Ⅲ)令
,若
,求所有
之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31837aec92b0162a04e9f58f8262fa30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca64ef9e0c3dd14e99d113dbbe973ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6227cce99354c34b73c9e49a286348d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf69bf5086355a30f15078f436abcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53864621c2e22d49665fcd192c838584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c18b66ea7fcc351a06f6bf6483f6fc.png)
(Ⅰ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcec0bc8c9ba2feb834e1ad5d0e4747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52bcfad9a2c32adbcbb4e0cd430baad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4d9c2efd5fbc471445c9b52984ee50.png)
(Ⅱ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a713dcfb247321b9b210164d28f2afef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53864621c2e22d49665fcd192c838584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5dc2e70c298b723c3f3b35381f53011.png)
(Ⅲ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abd07ce63b846e07579191990771816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a077bff58ed914f0fef9eba2c9095224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c18b66ea7fcc351a06f6bf6483f6fc.png)
您最近一年使用:0次
2016-11-30更新
|
772次组卷
|
6卷引用:北京市京源学校2017-2018学年高三十月月考数学试题
北京市京源学校2017-2018学年高三十月月考数学试题(已下线)2011届北京市丰台区高三下学期统一练习数学理卷(已下线)2013届中国人民大学附属中学高考冲刺五理科数学试卷2015届北京市第四中学高三上学期期中考试理科数学试卷(已下线)上海市华东师范大学第二附属中学2022-2023学年高一上学期开学考试数学试题(已下线)第6章 计数原理(基础、常考、易错、压轴)分类专项训练-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)