题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-99166.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-40827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063550-96827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063550-77940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063550-46915.gif)
Ⅰ.求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063550-90260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-78584.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-59200.gif)
Ⅱ.求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-29038.gif)
Ⅲ.证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-86018.gif)
答案
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063552-35263.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063552-88807.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063552-97882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063552-13255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063552-59273.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063553-61999.gif)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063553-11501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063553-55525.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063553-39252.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063554-95006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063554-45289.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063554-66623.gif)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063554-69141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063554-23981.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063555-39418.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063555-80804.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063555-77676.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063555-49888.gif)
由此知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063555-50731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063556-25955.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063556-46052.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063556-49897.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063556-56782.gif)
Ⅱ. 解:当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063552-97882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063557-42879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063557-27838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063557-93698.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063557-33140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-96422.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-52898.gif)
为求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-29038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-52179.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-82440.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-78161.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063559-40986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063559-80323.gif)
综上,当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-82440.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063559-81416.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063559-40986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063559-90259.gif)
Ⅲ. 证法一:首先证明当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-82440.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-42323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-82918.gif)
用数学归纳法证明:
(ⅰ)由Ⅱ知当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-45785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-71575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063601-77924.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063601-81074.gif)
(ⅱ)假设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063601-38198.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063601-47065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-82918.gif)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063601-95055.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063602-67617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063603-27870.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063603-72732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063603-17506.gif)
由(ⅰ)与(ⅱ)知,对所有自然数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063554-23981.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063603-68601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-82918.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-42323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-82918.gif)
其次,当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063604-88687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063604-53558.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063604-18498.gif)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063549-96164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-86018.gif)
证法二:首先证明当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063558-82440.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-42323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-82918.gif)
对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063604-45469.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-59200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063605-86438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063605-36336.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063605-39167.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063605-19579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063605-32759.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063606-82066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063600-82918.gif)
其次,当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063604-88687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063604-53558.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063604-18498.gif)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-29038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063551-86018.gif)
核心考点
试题【已知函数的图像是自原点出发的一条折线,当时,该图像是斜率为的线段(其中正常数),设数列由定义.Ⅰ.求、和的表达式;Ⅱ.求的表达式,并写出其定义域;Ⅲ.证明:的图】;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/20191013/20191013063543-38155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063544-89546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063544-26107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063544-89546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063544-59320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063544-43726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063543-38155.gif)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063544-94300.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063544-89546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063545-23284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063545-21507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063545-53476.gif)
(Ⅰ)求公差d的取值范围.
(Ⅱ)指出S1,S2,…,S12中哪一个值最大,并说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063520-50996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063520-72604.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063520-27771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063451-21515.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063451-18401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063451-67418.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063451-71417.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063452-82045.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063452-17870.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013063452-49303.gif)
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