题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035629-26969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035629-11420.png)
(1)求r的值;
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035629-45193.png)
(3)若对一切的正整数n,总有
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035629-74741.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035629-85499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035630-75586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035630-83177.png)
解析
试题分析:(1)由已知可得,
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035630-70077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035630-77915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035630-82856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035631-49097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035631-96799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035631-85519.png)
(2)由(1)可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035631-96623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035632-53853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035632-78103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035632-71633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035632-37697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035633-82398.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035633-25536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035633-64799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035633-94122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035633-81480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035634-46611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035634-65899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035634-75631.png)
所以一切的
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035634-81566.png)
点评:数列求和采用的错位相减法,此法适用于通项公式为关于n的一次式与指数式的乘积形式的数列,第三问不等式恒成立转化为求数列前n项和的最值,期间借助了数列的单调性
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035608-77546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035608-60471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035608-20476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035608-84767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035609-36869.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035605-93742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035605-22289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035559-76402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035559-82682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035559-76402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035559-64328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-77354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-39819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-82411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-90499.png)
① 不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-90499.png)
② 在定义域内存在
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-76254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035545-51862.png)
(1) 求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-90499.png)
(2) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035544-39819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035534-24244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035534-82042.png)
(1)试判断数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035534-54038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035534-40511.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035535-96213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035535-85692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035535-96213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035535-16974.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035535-28349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035535-82461.png)
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