题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060849-14230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060849-80562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060849-14230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060849-68845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060850-58927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060850-93695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060850-90657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-64706.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-46238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-44304.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-87886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-12478.png)
(3)求证:存在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-54613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-38891.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-56801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060853-21260.png)
解析
试题分析:本题是一道新定义题,主要考查归纳推理、数学归纳法、分类讨论思想等基础知识,考查学生的分析问题解决问题的能力和转化能力.第一问,由于
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060849-80562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060853-57242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060853-19981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060849-80562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060850-58927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060853-36777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060854-50208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060850-58927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060854-50208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-54613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-38891.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060853-57242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060853-19981.png)
(2)假设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060850-58927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060854-97387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060854-64294.png)
那么可以设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060855-62272.png)
其中
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060855-56650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060855-55751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060855-99052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060856-95690.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060853-36777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060856-32890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060856-82263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060856-25699.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060857-85407.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060856-95690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060857-97396.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060857-29930.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060857-65970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-12478.png)
(3)由(2)可知当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-87886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060851-12478.png)
同理当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060858-66241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060858-78857.png)
若不存在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-54613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-38891.png)
则对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060850-90657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060858-66241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060858-78857.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060858-59665.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060858-56899.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060859-43563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060859-95904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060858-66241.png)
存在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-54613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060852-38891.png)
核心考点
举一反三
1=1
2+3+4=9
3+4+5+6+7=25
4+5+6+7+8+9+10=49
照此规律,第五个等式应为 .
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060835-84761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060835-15307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060835-54400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060830-25263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060831-97475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060831-68684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060831-54604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060826-78373.jpg)
则在第n个图形中共有( )个顶点。
A.(n+1)(n+2) | B.(n+2)(n+3) | C.![]() | D.12n |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106060821-34524.png)
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