题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013502-64463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013502-99105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013502-73763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013503-16279.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013502-64463.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013503-79773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013503-72179.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013504-60345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013504-81740.png)
解析
试题分析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013504-74738.png)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013504-51427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013505-51139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013505-94761.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013505-78099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013505-85874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013506-99755.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013506-90913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013506-13435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013507-62754.png)
易知:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013503-72179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013507-79241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013507-23375.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013504-81740.png)
点评:求数列的通项公式和数列的前n项和是数列中常见题型。这儿求数列的前n项和用的是裂项法。常见的裂项公式:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013507-81388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013508-40254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013508-38647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013508-34273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013508-69857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013509-62387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013509-44969.png)
核心考点
举一反三
(2,2),(3,1),(1,4),(2,3),(3,2),(4,1),(1,5),
(2,4)…,则第57个数对是
在数列{an}中,a1=1,an=n2[1+
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013417-65243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013417-94799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013417-85902.png)
(1)当n≥2时,求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013418-71468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013418-58877.png)
(2)求证:(1+
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013418-76323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013418-15137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013419-16252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013338-89292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013338-92290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013338-35940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010013328-88801.png)
A.±![]() | B.±![]() | C.-![]() | D.![]() |
A.6 | B.7 | C.5或6 | D.6或7 |
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