题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093206-38658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093206-50102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093206-80892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093206-81156.png)
(1)猜测并直接写出
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093207-28464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093207-72380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093207-11684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093207-98868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-89792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-47315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-93217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-43067.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-86462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093209-67792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093209-26473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093209-12861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093209-66961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093210-74620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093210-67510.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093210-75168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093210-65874.png)
②设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093210-45465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-86462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-78466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-78466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-42037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-35614.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-17367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-52056.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093212-88951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093212-33892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093212-29889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093212-59901.png)
然后再讨论二次函数的对称轴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093213-62550.png)
(2)在(1)的基础上,可得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093213-69992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093213-40793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093213-43707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093214-88457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093214-13174.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093214-45392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093214-87325.png)
解:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093214-92966.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093215-82707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093215-80543.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093212-33892.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093215-36034.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093215-69169.png)
ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093216-48335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093216-52508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093212-59901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-47315.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093216-72030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093216-15297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093216-27128.png)
ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093217-39541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093217-80465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093217-83003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093217-75007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093217-75007.png)
(2)①由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093218-58932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093218-25040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093218-10621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093218-66299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093219-67096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093208-86462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093219-89573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093210-75168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093219-90191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093219-86986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093219-49474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093220-52742.png)
②-①得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093220-56978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093220-80268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093220-86450.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093221-45436.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093221-83443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-42037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093221-31842.png)
注意到,当n为奇数时,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093221-32762.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-78466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093221-76409.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093222-14549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093222-13305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093222-12444.png)
对于任意的正整数n都有
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093221-31842.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093222-73719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093211-52056.png)
核心考点
试题【已知函数,设,. (1)猜测并直接写出的表达式;此时若设,且关于的函数在区间上的最小值为,则求的值;(2)设数列为等比数列,数列满足,,若 ,,其中,则①当时】;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/20191012/20191012093146-89690.png)
⑴当a1=1,c=1,d=3时,求数列{an}的通项公式
⑵当0<a1<1,c=1,d=3时,试用a1表示数列{an}的前100项的和S100
⑶求证:当0<a1<
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093146-69678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093146-69678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093146-69678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093146-69678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093146-69678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093146-69678.png)
A.8 | B. 11 | C. 12 | D. 15 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093117-98287.png)
(1)求数列{bn}的通项公式;
(2)在平面直角坐标系内,直线ln的斜率为bn,且与抛物线y = x2有且仅有一个交点,与y轴交
于点Dn,记
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093118-48035.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093118-68701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093056-73252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093056-86925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093056-68638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093056-84988.png)
(Ⅰ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093057-60422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093057-64244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093057-68649.png)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093056-86925.png)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093057-46468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012093058-39402.png)
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