题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043057-72932.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043058-92387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043058-49072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043058-57193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043058-85171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-87678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-60369.gif)
(Ⅰ)证明:对任意的实数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-87678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043057-72932.gif)
(Ⅱ)证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-15512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043058-92387.gif)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-41867.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043058-92387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-60369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-87678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-60369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-22980.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-87678.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-87678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043057-72932.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043100-10473.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043100-82819.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043057-72932.gif)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043100-26417.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043100-23582.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043101-28408.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043101-28966.gif)
故当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-15512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043058-92387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043101-93729.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043101-26997.gif)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-15512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043101-31798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043102-35990.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043102-35806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043102-17715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043102-57342.gif)
要使对任意正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-60369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-22980.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043103-57469.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043103-24823.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-60369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043103-25367.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-60369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043103-80647.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043103-50254.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043104-11170.gif)
于是可得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043104-75659.gif)
综上所述,存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-87678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-60369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043104-92660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043059-87678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043104-74103.gif)
解析
核心考点
试题【已知数列和满足:,,,其中为实数,为正整数。(Ⅰ)证明:对任意的实数,数列不是等比数列;(Ⅱ)证明:当时,数列是等比数列;(Ⅲ)设为数列的前项和,是否存在实数,】;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/20191011/20191011043042-63828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043042-24366.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043042-35019.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043042-37671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043043-70864.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043042-24366.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043043-29564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043043-45217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043043-99945.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043043-29564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043043-95642.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043044-70192.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043042-24366.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043044-14492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043037-99869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043022-90023.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043022-90023.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043022-90023.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043022-80088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043022-97575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043022-56630.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043022-91824.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043023-97437.jpg)
求:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043023-26757.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043023-75979.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043023-10265.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043024-42377.gif)
(3)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043024-46725.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043024-19758.gif)
(4)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043024-68060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011043025-44797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-26795.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-73328.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-31335.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-61389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-28955.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042946-58377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-61389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042946-71838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042946-99045.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-61389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042946-24978.gif)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042946-27081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042947-91351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042947-15582.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-61389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042947-69255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042947-19647.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042945-61389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042958-95437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042958-52221.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042959-89772.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042958-52221.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042915-29701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042915-23205.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042915-92629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042915-89026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042916-18189.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042916-82056.gif)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042916-11552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042916-44437.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042916-95088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042917-99766.gif)
(Ⅲ)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042917-84169.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042917-72207.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011042917-73975.gif)
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