题目
题型:不详难度:来源:
第3小题满分8分.
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035742-42152.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035742-58393.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035742-83410.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035743-40536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035743-17466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035743-92292.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035743-11787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035743-48898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035744-20935.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035744-73708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035744-67558.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035744-80684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035743-92292.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035744-43259.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035745-20879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035745-11857.gif)
(2)求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035743-92292.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035745-10550.gif)
(3)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035745-73569.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035746-18651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035746-48345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035746-83763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035746-17802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035746-84083.gif)
求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035745-11857.gif)
答案
(2)证明见解析.
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035747-30370.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035747-38174.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035747-84381.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035747-50879.gif)
(2)证明:用数学归纳法证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035747-26390.gif)
① 当n=1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035748-13951.gif)
② 假设n=k时等式成立,即
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035748-14805.gif)
那么当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035748-90690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035748-41072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035748-46958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035749-49084.gif)
根据①和②可以断定:当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035747-26390.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035749-24482.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035749-77495.gif)
∵ 4m+1是奇数,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035749-56550.gif)
∴这些项均不可能取到100. ………………………..15分
此时,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035747-30370.gif)
核心考点
试题【(本题满分18分)本题共有3个小题,第1小题满分4分,第2小题满分6分,第3小题满分8分.已知数列:,,,(是正整数),与数列:,,,,(是正整数).记.(1)】;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/20191013/20191013035735-13269.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035735-50739.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035735-76571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035735-17879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035736-31390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035736-71192.gif)
(文科10分)设0<a,b,c<1,求证:(1-a)b,(1-b)c,(1-c)a不同时大于
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035736-22126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035730-88792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035730-58502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035730-50670.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035730-62944.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035711-24367.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035712-76186.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035712-45463.gif)
(I)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035712-92563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035711-24367.gif)
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035712-96392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035712-79696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035713-83996.gif)
求使
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035713-19439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035706-34597.gif)
A.1 | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035653-15832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035653-32452.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035653-82752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035653-59509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035653-22595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035654-73418.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035654-63977.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035654-92774.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035654-77129.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035655-49285.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035655-16410.gif)
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