题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014717-87777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014717-89791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014724-71560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014717-87777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014724-72070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014717-87777.gif)
(Ⅰ)求证:M点的纵坐标为定值;
(Ⅱ)若Sn=f(
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014724-81128.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014724-84375.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014724-37386.gif)
(Ⅲ)已知数列{an}的通项公式为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-95113.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-97187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-97187.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014717-87777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-44388.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-69847.gif)
即x1+x2="1."
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014726-43087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014726-83647.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014726-71666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014726-21072.gif)
即M点的纵坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014727-67608.gif)
(Ⅱ)当n≥2时,
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014724-37386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014727-79914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014727-60658.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014727-10381.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014727-93432.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014728-55533.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014728-53473.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014728-75659.gif)
∴2Sn=n-1,则
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014728-52171.gif)
(Ⅲ)由已知T1=a1=
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014729-24544.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014729-35803.gif)
∴Tn=a1+a2+…+an=
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014729-31652.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014730-72209.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014730-53114.gif)
当n∈N+时,Tn<
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-97187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-97187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014730-87969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-97187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014730-53366.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014730-40891.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014731-77760.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014725-97187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014717-87777.gif)
解析
核心考点
试题【 (本题满分16分)A、B是函数f(x)=+的图象上的任意两点,且=(),已知点M的横坐标为. (Ⅰ)求证:M点的纵坐标为定值; (Ⅱ)若Sn=f()+f()+】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014711-13740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014711-78536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014712-92329.png)
A.180 | B.240 | C.360 | D.720 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014642-90096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014643-21533.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014643-32298.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014643-56512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014643-19380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014643-40890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014644-95972.gif)
(I)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014642-90096.gif)
(II
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014644-66274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014642-90096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014643-21533.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014643-32298.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014436-72166.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014436-11598.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014436-33692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014437-13023.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014437-53699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014437-56412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014437-70836.gif)
(Ⅱ)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014437-40764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014438-63376.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014448-12744.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014448-56815.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014331-14388.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014331-61563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014331-16655.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014331-40961.gif)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014331-14388.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014331-80274.gif)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014332-74377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014332-90019.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014331-61563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014332-13875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014332-83095.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014333-19507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014333-66199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014317-93965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014317-33543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011014318-50594.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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