题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-81816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-91449.png)
答案
证明:(1)当n=1时,点P1是直线y=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-75505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-81816.png)
∴可求出P1(
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-33171.png)
∴a1=|OP1|=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-48643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-48643.png)
(2)假设n=k(k∈N*)时命题成立,即a1+a2+…+ak=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
∴直线QkPk+1的方程为y=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-75505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-81816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-72785.png)
∴ak+1=|QkPk+1|=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-33171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142159-41358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-48643.png)
∴a1+a2+…+ak+a k+1=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142158-48643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142157-89214.png)
∴当n=k+1时,命题成立.
由(1)(2)可知,命题对所有正整数都成立.(13分)
解析
核心考点
试题【设P1,P2,P3,…,Pn,…是曲线y=上的点列,Q1,Q2,Q3,…,Qn,…是x轴正半轴上的点列,且△OQ1P1,△Q1Q2P2,…,△Qn-1QnPn,】;主要考察你对抛物线的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142150-43228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142132-20138.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142117-79809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142117-63991.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142117-68669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142117-70681.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142117-79809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142118-98826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142118-34796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142118-98826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142118-34796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142118-19694.gif)
(1)求抛物线的标准方程;
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142118-32811.gif)
(3)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142119-54788.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142119-92823.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142119-13894.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142110-10951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142110-93467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142110-31448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142111-47607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142111-10832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142110-93467.png)
(1) 求证: OA^OB;
(2) 当△OAB的面积等于
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025142055-69086.png)
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