题目
题型:不详难度:来源:
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035331-35576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035331-33605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035332-37843.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035332-89348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035332-45659.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035332-23238.gif)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035333-86490.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035333-93307.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035333-94093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035332-45659.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035333-23494.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035331-35576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035333-30692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035334-98984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035334-61432.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035334-76034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035334-80011.gif)
显然n=1时也适合.所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035335-86218.gif)
(Ⅱ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035334-98984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035335-86218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035335-48479.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035335-10142.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035335-86500.gif)
两式相减得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035336-43087.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035336-12372.gif)
解析
核心考点
举一反三
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035302-94513.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035302-48784.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035302-56106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035303-53633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035303-58199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035303-20830.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035303-20585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035304-75748.gif)
(1)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035304-33475.gif)
(2)求数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035304-47024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035304-35233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035304-60357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035305-71409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035305-39261.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035304-75748.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035305-44458.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035305-71409.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035305-53676.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035304-75748.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035306-90143.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035306-90666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035303-58199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035306-14468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035255-85012.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035256-10009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035256-59148.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035256-19069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035256-29450.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035257-10576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035257-45648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035257-42996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035257-23867.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035257-95557.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035256-10009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035256-19069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035258-41623.gif)
如:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035258-30486.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035258-66010.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035258-11785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035259-80467.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035221-53723.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035221-71020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035221-56575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035221-16498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035221-56575.gif)
n项和为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035222-13263.gif)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035222-93989.gif)
(2) 求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035222-18585.gif)
(3) 抽去数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035221-53723.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035222-94267.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035222-94267.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035223-32998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035223-20035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035212-34105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035212-23928.gif)
(1) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035212-95552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035212-36852.gif)
(2) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035212-25823.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035207-46151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035207-91325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035207-93669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035208-37014.gif)
那么
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013035208-53653.gif)
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