题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211907-23011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211907-48259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-67801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-80835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-99221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-93605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-67801.png)
(1)判断数列
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-59012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-36668.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-67801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-18923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-80835.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-69420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-91782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-46473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-89217.png)
均构成“Γ数列”,求
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-69420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-91782.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-59012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-36668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-95823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-75099.png)
解析
试题分析:(1)判断数列
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-59012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-36668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-80835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-99221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-99221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-59012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-19265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-80430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211912-24858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-36668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211912-40210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211912-43267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-67801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-18923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211908-80835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211912-76444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211912-29237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-43059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-72165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-69420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-91782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-34905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-75099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-94119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-75099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-94119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-61534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-72902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-90816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-75099.png)
(1)①因为
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211915-74546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-59012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
②因为
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211915-21161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211915-58618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-36668.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211909-36668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
(2)反证法证明:
假设存在某项
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211912-76444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211912-29237.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211915-55381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211916-20383.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211916-52223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-72165.png)
这与“
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
(3)由(2)问可知
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-34905.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-75099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211916-14394.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-94119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211916-47051.png)
由“
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211910-42996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211917-61147.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-72902.png)
显然当
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-90816.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211913-94119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211917-73814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211914-72902.png)
综上讨论可知
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-95823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211911-75099.png)
核心考点
试题【给定正整数,若项数为的数列满足:对任意的,均有(其中),则称数列为“Γ数列”.(1)判断数列和是否是“Γ数列”,并说明理由;(2)若为“Γ数列”,求证:对恒成立】;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/20191008/20191008211827-83045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211827-67363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211827-39193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211827-20270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211828-34681.png)
A.2011 | B.2012 | C.4022 | D.4023 |
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211729-15628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211729-18611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211729-90751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211729-53724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211729-13706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211730-69228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211730-67776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211722-42034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211722-81593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211723-51045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211723-65925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211723-51729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211723-92866.png)
A.1 | B.2 | C.4 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211623-45609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211624-24744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211624-63947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211624-16349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211625-33181.png)
A.![]() | B.![]() | C.![]() | D.![]() |
方案一:每天回报40元;
方案二:第一天回报10元,以后每天的回报比前一天多回报10元;
方案三:第一天回报0.4元,以后每天的回报是前一天的两倍.
若投资的时间为
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008211504-21738.png)
A.方案一 | B.方案二 | C.方案三 | D.都可以 |
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