题目
题型:不详难度:来源:
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011245-48546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011245-88157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011246-96236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011246-17882.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011246-26912.png)
(2)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011246-29752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011247-76193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011247-62062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011247-86468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011245-88157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011247-21912.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011248-37041.png)
(2)先“错位相减法”求和,放缩即得
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011248-38934.png)
解析
试题分析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011248-77332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011248-10401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011249-43135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011249-43305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011249-73143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011249-28782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011249-88415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011250-87921.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011250-20592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011250-43388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011250-91604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011251-52880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011251-65590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011251-99437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011251-84958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011252-78053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011252-60244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011252-76340.png)
点评:中档题,本题具有较强的综合性,本解答从确定通项公式入手,进一步认识数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011247-86468.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011205-84380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011205-65734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011206-51661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011206-44135.png)
已知等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011000-15671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011000-44907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011000-15671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011001-98605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011001-14350.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011001-11949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011001-14350.png)
(Ⅱ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011001-47501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011002-41222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011001-98605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011002-85417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010011002-66188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010939-47568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010940-30844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010941-82155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010941-70004.png)
A.![]() | B.![]() | C.-5 | D.5 |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010615-20322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010615-64989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010615-27342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010615-62463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010615-27556.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010550-46940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010550-99521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010550-97742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010550-84335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010551-66207.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010550-46940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010550-97742.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010551-68354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010551-64215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010551-33888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010552-36153.png)
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