题目
题型:不详难度:来源:
(本小题共13分)
用
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082612-11914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082612-90037.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082612-73374.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082612-60396.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082613-70848.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082613-97603.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082613-32585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082613-37844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-75038.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-33073.gif)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-97223.gif)
(Ⅲ)求证:在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-75038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-81900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-95109.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082615-37735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082615-96567.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082615-99292.gif)
(Ⅱ)因为数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-75038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082615-50120.gif)
所以我们可设计如下表格
![]() | 1 | 2 | 3 | 4 | 5 | ‥‥ | ![]() |
1 | ![]() | ![]() | ![]() | ![]() | ‥‥ | | ‥‥ |
2 | ![]() | ![]() | ![]() | ![]() | ‥‥ | | |
3 | ![]() | ![]() | ![]() | ‥‥ | ‥‥ | | |
4 | ![]() | ![]() | ![]() | ‥‥ | ‥‥ | | |
5 | ![]() | ![]() | ![]() | ‥‥ | ‥‥ | | |
且
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082616-11957.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082617-32749.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082618-30661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082619-77769.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082619-51144.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082616-63481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082617-96187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082618-98740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082616-69237.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082619-10654.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-48747.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-83636.gif)
(Ⅲ)任取
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082620-37832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082621-23786.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082621-16709.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082621-35055.gif)
即在(Ⅱ)表格中不会有两项的值相等.
对于
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-81900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082621-95687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-81900.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082621-95687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082616-11957.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082622-11819.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082621-95687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082622-62791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082621-95687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082622-92255.gif)
同理,第二行共有
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082622-11111.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-81900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082622-11111.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082623-12911.gif)
第
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082623-64002.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082623-84878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-81900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082623-84878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082623-14869.gif)
∴在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-75038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082614-81900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082624-27483.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082624-54115.gif)
解析
核心考点
试题【(本小题共13分)用表示不大于的最大整数.令集合,对任意和,定义,集合,并将集合中的元素按照从小到大的顺序排列,记为数列. (Ⅰ)求的值;(Ⅱ)求的值; (Ⅲ)】;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/20191011/20191011082542-65928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082542-99433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082542-54792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082542-74902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082542-65928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082543-81631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082543-44014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082543-48142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082449-61873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082450-22181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082450-58710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082450-59614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082450-59614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082450-58710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082450-45199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082450-38349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082451-15762.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082451-59885.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082451-68624.gif)
(Ⅰ) 若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082451-64621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082452-26926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082452-31703.gif)
(Ⅱ) 若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082452-31495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082452-32409.gif)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082452-31495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082452-50390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082453-42924.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082453-14135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082453-42924.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082453-95033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082431-48980.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082431-25415.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082432-98235.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082432-82409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082432-20265.gif)
(1)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082432-39503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082433-16421.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082432-39503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082433-40172.gif)
(2)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082433-32712.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082433-61239.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082433-32712.gif)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082433-37300.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082434-88872.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082434-27323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082432-98235.gif)
若不存在,请说明理由.(8分)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082409-85257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082409-56977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082409-35913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082410-13792.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082402-13343.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082403-23181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082403-74331.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082403-37039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082403-37039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082403-44754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082404-78298.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011082404-85306.gif)
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