题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020528-63235.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020528-45412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020528-81541.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020528-82392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-97016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-61478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-43149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-78256.gif)
⑴求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020530-94870.gif)
⑵求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020528-63235.gif)
⑶若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020530-67862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020530-40149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-33122.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-61478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-56256.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-29686.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-79016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-61478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-91495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-61478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-29686.gif)
答案
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020532-74621.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020532-80067.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020532-83083.gif)
化简得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020532-21553.gif)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020533-49758.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-61478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020533-76467.gif)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020530-94870.gif)
⑵由⑴知等比数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020530-94870.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020533-60970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020533-23046.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020533-11037.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020533-84318.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020532-74621.gif)
⑶当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020534-75348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020534-83928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020534-50909.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020534-94802.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020535-47164.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020535-86321.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020535-76343.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020535-29557.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020535-83337.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020536-37822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-91495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020536-62706.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020536-58320.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020529-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-91495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020536-16078.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020537-57576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020537-26182.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020537-46227.gif)
∴当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020532-80067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020537-80699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020537-72439.gif)
综上所
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020528-45412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020537-72439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020532-80067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020531-91495.gif)
核心考点
试题【已知数列中,,且,其前项和为,且当时,.⑴求证:数列是等比数列;⑵求数列的通项公式;⑶若,令,记数列的前项和为.设是整数,问是否存在正整数,使等式成立?若存在,】;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/20191013/20191013020516-27786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020516-27786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020516-54305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020516-60716.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020517-99455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020517-51977.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020517-33970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020517-99455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020517-34294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020518-84028.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020517-99455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020518-65292.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020518-91193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020503-98154.gif)
若一个数列各项取倒数后按原来的顺序构成等差数列,则称这个数列为调和数列.已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020504-95615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020504-26499.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020504-82026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020504-77116.gif)
(Ⅰ)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020504-26499.gif)
(Ⅱ)把数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020504-26499.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020505-41955.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020505-63766.gif)
(Ⅲ)对于(Ⅱ)中的数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020504-26499.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020505-72861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020505-83231.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020505-72861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020453-18283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020454-15154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020454-71016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020454-80375.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020454-35191.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020446-33705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020446-14568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020447-68463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020447-83132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020447-96098.gif)
(Ⅰ)求证:{
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020447-15303.gif)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020446-33705.gif)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020447-39373.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020448-61821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020439-47312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020439-24740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020439-58840.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020439-47312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020439-19154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013020440-77395.gif)
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