题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234813-77646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234813-64840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-99986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-58424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-14584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-43650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-90872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-43650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-90872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234815-90102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234815-87855.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234815-35417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234815-81157.png)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234813-77646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234813-64840.png)
(Ⅲ)证明:对一切正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234816-89257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234816-61080.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234816-82389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234816-98344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-96945.png)
解析
试题分析:(Ⅰ)依题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-16562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-77755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-99986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-58424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234815-35417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234815-81157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-16562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-77755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-50518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-91141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-16695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-95207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-43650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-48191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-52152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-96945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-16695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-95207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234816-98344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-95207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234819-53430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234819-88390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234814-14584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234825-63404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234825-69744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234816-89257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234825-68939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234825-39524.png)
试题解析:(Ⅰ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234826-35535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234826-46586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234826-94364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234826-35521.png)
(Ⅱ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234826-95010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234827-98949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234827-69172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-16562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234827-98949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234827-69172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234827-85883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-77755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234827-89052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-57028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-91141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-21300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-16695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-48191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234818-52152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-70209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234817-96945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-21300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-46286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234819-53430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234819-88390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-72381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234816-98344.png)
(Ⅲ)由(Ⅱ)可知,所证明的不等式为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234829-52599.png)
方法一:首先证明
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234829-44630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-21300.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234829-69326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234829-59161.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-21300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234829-22385.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234819-53430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-19844.png)
综上所述,对一切正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-72381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-50303.png)
方法二:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-29081.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-15052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234831-88494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234837-71233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234837-58482.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234819-53430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-19844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234837-76885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234837-34638.png)
综上所述,对一切正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-72381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-50303.png)
方法三:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234838-28226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234838-45825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234831-88494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234838-64162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234838-53762.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234819-53430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-19844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234837-76885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234837-34638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234838-82411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234839-58526.png)
综上所述,对一切正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234828-72381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234830-50303.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234804-12812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234804-59624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234805-69654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234805-99210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234753-15178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234753-99865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234753-99299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234753-63731.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234753-99865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234753-15178.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234753-59886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234754-97378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234754-28674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234754-40869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234737-82261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234737-10505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234738-67078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234738-25626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234722-20270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234722-52371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234723-68945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234723-78313.png)
A.36 | B.42 | C.45 | D.63 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234647-88146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234647-86725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234647-72575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234648-78307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234648-15849.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234647-72575.png)
(2)若从
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234647-88146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234648-47145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234648-81036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234648-45111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234649-80430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234649-84647.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234648-47145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234649-12657.png)
②若关于
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234649-38127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234649-28232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011234648-47145.png)
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