题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041926-61517.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041926-79214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041926-80597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041926-75476.gif)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041926-79214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041927-88260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041927-19324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041926-79214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041927-61551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041927-55830.gif)
(1)若k=1,求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041927-29239.gif)
(2)项m=2,问是否存在常数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041928-61386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041928-78817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041928-67254.gif)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041928-31520.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041927-29239.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041928-15911.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041929-25588.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041929-10428.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041929-75945.gif)
解析
(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041929-83564.gif)
所以其值域为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041930-50342.gif)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041930-83046.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041930-10113.gif)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041930-18423.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041930-10676.gif)
法一:假设存在常数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041928-61386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041931-90750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041931-44225.gif)
法二:假设存在常数k>0,使得数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041928-78817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041931-73248.gif)
当k=1不符合。……9分
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041931-26789.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041931-78803.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041932-68748.gif)
(3)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041932-92134.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041926-79214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041932-91896.gif)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041932-30265.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041933-71349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041933-72493.gif)
则有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041933-95742.gif)
进而有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041933-59609.gif)
核心考点
试题【 已知函数时,的值域为,当时,的值域为,依次类推,一般地,当时,的值域为,其中k、m为常数,且(1)若k=1,求数列的通项公式;(2)项m=2,问是否存在常数,】;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/20191013/20191013041912-13466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041913-84435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041913-25848.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041912-13466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041905-26506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041905-91730.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041905-78841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041905-26506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041906-73257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041857-20165.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041857-71148.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041857-21779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041858-27439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041858-41485.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041858-96107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041858-19661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041859-62699.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041859-88047.gif)
(2)求证
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041859-39447.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041851-49629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041851-83024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041851-87653.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041852-25973.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041852-62413.gif)
A.16 | B.24 | C.36 | D.48 |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041847-89214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041847-29201.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041848-28878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041848-17507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041848-81483.gif)
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