题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093509-97958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093509-76467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093509-47301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093509-97958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-59993.png)
(Ⅰ)求通项公式
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-35230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-59993.png)
(Ⅱ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-52858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-16936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-16388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-94648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-23393.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-13840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-59993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-60833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-48410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-23393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-43113.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093509-76467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093509-47301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-37108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-56893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-37108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-56893.png)
(II)由(I)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-52858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-16936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-30552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-53900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093513-46372.png)
解:(Ⅰ)设等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093509-97958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093513-19610.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093513-27380.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-13840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-59993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-60833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-48410.png)
(Ⅱ)由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093513-26638.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-52858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-16936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-30552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093512-53900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093513-46372.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-23393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093513-12640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093514-58788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-43113.png)
即数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093510-94648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-23393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093511-43113.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093448-60541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093448-42528.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093448-60541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093448-72510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093448-11275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093448-72510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093448-40887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093449-33800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093449-90246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093431-34202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093432-65701.png)
其中
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093432-60977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093432-22449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093432-52655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093432-95183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093432-17796.png)
已知等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093422-45326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093423-25200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093423-54173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093422-45326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093423-85283.png)
(Ⅰ)求通项公式
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093423-86077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093423-85283.png)
(Ⅱ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093423-48499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093424-94985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093424-54263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093424-44877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093425-88963.png)
已知等差数列{an}中,a1=-1,前12项和S12=186.
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)若数列{bn}满足
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093410-44690.png)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093410-27505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093404-11820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093404-71458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093404-22251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093405-92764.png)
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