题目
题型:不详难度:来源:
集合
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-10161.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25451.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-44590.gif)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-13434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-64391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-95440.gif)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-76941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031024-25279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031024-14121.gif)
为了表示这些子集,作
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031024-88474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031024-68259.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031025-98449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031025-66829.gif)
(1)该表中每一列至少有多少个1;若集合
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031025-89178.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031025-98943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031025-84225.jpg)
(2)用含
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031024-88474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031026-67748.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031026-42431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031026-21230.gif)
(3)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031026-48617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031026-42431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-66556.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-22333.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-10514.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-32065.gif)
答案
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-84721.gif)
(3)证明见解析。
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-64391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031025-98943.gif)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
2 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
![]() | 1 | 1 | 0 | 0 | 0 | 1 | 0 |
4 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
5 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
6 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
7 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
(2)题设条件①中的
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-13434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031028-26648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031028-38097.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-84721.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-64391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031024-88474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031024-88474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031022-25644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031028-60334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031028-17695.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031026-21230.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031029-80071.gif)
检验
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031029-60496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031029-33146.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031029-95715.gif)
证法一:要证:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-10514.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031030-95087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031030-36581.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031030-60106.gif)
故只要证:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031030-90527.gif)
即只要证
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031023-95440.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031030-13523.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031031-75386.gif)
所以命题得证。
证法二:同上
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031029-95715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031031-94648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031031-91997.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031031-43645.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031032-93098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031027-10514.gif)
核心考点
试题【(本题满分 13分)集合为集合的个不同的子集,对于任意不大于的正整数满足下列条件:①,且每一个至少含有三个元素;②的充要条件是(其中)。为了表示这些子集,作行列】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031016-70928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031017-11323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031017-81456.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031017-81456.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031017-98986.gif)
A.11 | B.17 | C.19 | D.21 |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031010-36828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031011-50551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031011-29888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031011-50551.gif)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031010-36828.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031011-21946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031011-92216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031011-15561.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031002-74149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031002-39577.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031002-28903.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031003-12133.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031003-92802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031003-88738.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013031002-39577.gif)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030951-63505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030951-84509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030951-91455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030952-63876.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030952-88864.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030952-71489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030952-41145.gif)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030951-63505.gif)
(Ⅲ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030953-97666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030953-28902.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013030953-42467.gif)
(1)证明:数列{an+1-an }是等比数列;
(2)求数列{an}的通项公式
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