题目
题型:不详难度:来源:
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050302-93233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050303-45196.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050303-39549.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050303-56922.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050303-39549.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050303-93756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-39830.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-26362.gif)
在,求出实数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-39830.gif)
答案
(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-43459.gif)
(Ⅱ)当0<m<
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-48690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-26362.gif)
解析
(Ⅰ)由题意
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-75896.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050305-57749.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050305-55839.gif)
①式两端同乘以2,得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050305-35351.gif)
②-①并整理,得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050305-32696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050306-50146.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050306-55534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050306-80479.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050306-15539.gif)
(Ⅱ)由题意
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050307-61202.gif)
要使
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050307-21803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050307-78535.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050307-82181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050307-78535.gif)
①当m>1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050307-56388.gif)
②当0<m<1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050308-27947.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050308-37562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050307-78535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050308-76976.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050308-63392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050309-56065.gif)
综上,当0<m<
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-48690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050304-26362.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050250-15081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050250-51490.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050251-32121.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050251-84039.gif)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050251-20940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050251-52326.gif)
(1) 试求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050250-15081.gif)
(2) 若令
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050251-20136.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050252-82138.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050252-66889.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050252-62249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050230-69005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050230-93153.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050230-14034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050230-75928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050230-93153.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050231-97280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050231-17594.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050230-14034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050225-91280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050225-38034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-30925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-98862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-54799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-12099.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050209-71482.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050209-53851.gif)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-30925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050209-69727.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-54799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-12099.gif)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050209-45430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050208-54799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050209-96828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050148-44792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050148-72805.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050148-80816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050148-16624.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050149-59549.gif)
(Ⅰ)证明数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050149-41337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050148-44792.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050149-21758.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050149-11148.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050148-72805.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050150-67891.gif)
(Ⅲ)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013050148-44792.gif)
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