题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024933-64039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024933-62914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-38053.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-37472.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-40831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-58788.gif)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-69985.gif)
(Ⅱ)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024935-49614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024935-92930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024935-96906.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024935-32149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-11026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-69522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-85794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-85794.gif)
(Ⅲ)在(Ⅱ)的条件下,证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-43682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-69522.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-59587.gif)
(II)见解析通项公式为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024937-98247.gif)
(Ⅲ)见解析
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024933-62914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024937-22352.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-38053.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024937-52603.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-37472.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024937-51068.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024934-40831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024937-78134.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024938-61956.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024938-74400.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024938-50775.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024938-80803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-59587.gif)
(Ⅱ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024935-92930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024935-32149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024938-55235.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024939-98421.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024939-27998.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024939-38264.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024939-56371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-96502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-96502.gif)
∴有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-92304.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-19286.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-34556.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024936-85794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-96502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-96502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024937-98247.gif)
(Ⅲ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024940-29776.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024941-50118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024941-83344.gif)
核心考点
试题【已知函数满足,,;且使成立的实数只有一个。(Ⅰ)求函数的表达式;(Ⅱ)若数列满足,,,,证明数列 是等比数列,并求出的通项公式;(Ⅲ)在(Ⅱ)的条件下,证明:,】;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/20191013/20191013024921-99873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024921-49670.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024921-51736.gif)
(1) 证明数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024921-99873.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024921-30142.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024922-59706.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024922-10975.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024905-69010.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024905-57801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024905-16305.gif)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024905-69010.gif)
(Ⅱ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024906-27930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024906-80161.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024906-91763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024858-24512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024858-62819.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024858-93314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024858-46238.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024859-71577.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024837-82869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024837-33845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024837-79009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024838-51825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024838-18100.gif)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024837-82869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024837-33845.gif)
(2)若等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024837-82869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024838-50081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024838-21662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024834-10891.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024834-88530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024834-80266.gif)
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