题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-83980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000507-86070.png)
(1)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
(2)证明:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000507-53184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000507-51324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000507-86070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000507-31250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000508-51469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000508-82163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-39018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-85596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-60437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-47915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-24993.png)
解析
试题分析:(1)这个问题可以用特殊值法,数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-50042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-20201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000516-44620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000516-52802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-20201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000516-34479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000516-25733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000516-12328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-50042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000527-60216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000527-60216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000527-60216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000528-48641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000508-82163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000534-82672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000534-82672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000534-89902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000534-66710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000534-82672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000535-68344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000535-34653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000535-95072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000535-23645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000536-99431.png)
试题解析:(1)解法一:由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000536-76863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000536-27323.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000536-83411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000537-62934.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000551-70507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000552-34736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000552-84184.png)
所以,数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-39018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-85596.png)
解法二:因为数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000552-21977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000552-16900.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000553-23203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000553-97574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000553-67338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000552-84184.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000553-61119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000551-70507.png)
所以,数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-39018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-85596.png)
(2)假设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000553-22567.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000554-17380.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000554-71320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000554-57187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000554-60183.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000555-95800.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000555-72920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000555-62511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000555-56017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000556-21561.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
(3)由题意,对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000507-86070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000556-45184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000556-45920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000556-78272.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000607-13528.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000535-34653.png)
于是,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000608-70573.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000608-73344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000608-27174.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000514-60437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-47915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000508-82163.png)
此数列的首项为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000608-70005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000609-50208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000609-44497.png)
因此,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000506-13678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000515-24993.png)
核心考点
试题【已知数列满足().(1)若数列是等差数列,求它的首项和公差;(2)证明:数列不可能是等比数列;(3)若,(),试求实数和的值,使得数列为等比数列;并求此时数列的】;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/20191012/20191012000439-40018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000439-27801.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000424-53235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000424-10964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000424-65275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000424-21089.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000424-53235.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000425-53005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000425-17849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000357-69528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000357-62034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000358-95807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000358-90147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000358-90681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000358-26620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000349-93407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000350-88799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000350-85756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012000335-64240.png)
(1)求{an}的通项公式;
(2)若Cn=an·bn,求数列{Cn}的前n项和Sn。
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