题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042414-89771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042414-88754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-19696.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-85439.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-73167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-55090.gif)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042414-89771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-43688.gif)
(3)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042416-67825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042416-90314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042416-96505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042416-36747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042416-90314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042416-96580.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-58764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-70772.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-28902.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-25776.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042418-89018.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042418-67675.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-19696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-58764.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042418-53798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042418-15466.gif)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-58764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-19696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-70772.gif)
(2)解:由于
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042418-10377.gif)
则有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042419-61378.gif)
②-①,得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042419-93724.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042415-19696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042419-11576.gif)
同样有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042419-17845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042419-35588.gif)
③-④,得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042420-57884.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042420-85857.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042420-16982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042420-55784.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042420-85857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042414-89771.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-28902.gif)
(3)解:由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-28902.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042421-93155.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042421-96753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042421-44538.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042421-12851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042421-82192.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042422-17705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042422-57942.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042422-25881.gif)
要使不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042416-36747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042422-75531.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042423-48257.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042423-22387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042423-12278.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042423-44838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042423-71151.gif)
所以,实数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042424-73050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042417-25776.gif)
核心考点
举一反三
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042403-17279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042404-13609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042404-71861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042404-67944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042404-70906.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042404-48338.gif)
(Ⅰ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042405-45125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042405-89297.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042405-13354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042404-48338.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042405-46446.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042351-25003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042351-99061.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042351-51698.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042352-40149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042352-51256.gif)
A.30 | B.45 | C.90 | D.186 |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042338-84885.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042339-34764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042339-59843.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042339-16550.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042339-34764.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042339-43117.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042340-55650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042340-26723.gif)
(Ⅲ)若数列{bn}满足
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042340-61617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042340-29127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042340-58126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042341-53011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042341-24539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042332-28390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042332-65016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042332-11320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042332-70907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042333-50704.gif)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042332-28390.gif)
(Ⅱ)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042332-28390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042333-29648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013042333-29784.gif)
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