题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-25426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-54914.gif)
(Ⅰ)证明:若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-81438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-56423.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-25426.gif)
(Ⅱ)若对一切
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-87561.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-51017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-81438.gif)
答案
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-90453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-69944.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060844-67406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060844-99528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060844-53188.gif)
则由递推关系得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060844-61087.gif)
根据数学归纳法,对任何
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-67125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-25426.gif)
(II)(方法一)由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-99272.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-93066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-69805.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-22191.gif)
另一方面,若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060846-35407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060846-54635.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060846-39167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060846-18695.gif)
根据数学归纳法,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060846-96347.gif)
综合所述,对一切
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-67125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-93066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-90453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-69944.gif)
(方法二)由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060847-20707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060847-41040.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-90453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-69944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060847-92941.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060847-36828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060842-25426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060848-60687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060848-97173.gif)
根据数学归纳法,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060848-14426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060848-60687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060848-50817.gif)
因此,对一切
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-67125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060845-93066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-90453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060843-69944.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060834-41697.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060835-82857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060835-76999.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060835-52664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060835-96410.gif)
⑴求常数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060835-77103.gif)
⑵求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060836-19981.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-13643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-50732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-30770.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-56307.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-64924.gif)
⑵已知
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-13643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-50732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060824-30770.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060825-76993.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060825-64751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060815-54669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060815-92142.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060816-15892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060816-15892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060816-89415.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060816-54831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060816-61752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060807-46930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060808-46016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060808-19857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060808-58021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060808-84663.gif)
⑴求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060808-46016.gif)
⑵数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060808-46016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060809-50348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060809-65713.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060809-50348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060809-50348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060745-50715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060745-99925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060745-95942.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
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