题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024008-43506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-46365.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-88894.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-95916.gif)
(1)试用
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-20814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-60489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-13335.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-95916.gif)
(2)利用(1)的结论求解:“已知
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024010-85334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024010-72726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-60489.gif)
(3)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024008-43506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024010-57439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024010-17599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024011-72728.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024008-43506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024011-96921.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024011-75389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024011-88521.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024011-53030.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024008-43506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024012-39872.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024012-66496.gif)
解析
(1)解:不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024012-59088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024012-94868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024012-72258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024013-98984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024013-83087.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024013-90847.gif)
(2)(文科)解法一:由条件,可得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024013-13951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024013-27522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-67970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-29711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-48036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-35103.gif)
解法二:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024015-63777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-29711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024015-81543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024015-71469.gif)
(理)由条件,可得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024015-52671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024015-77459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024016-82283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024016-13160.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024010-72726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-29711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024016-80794.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024013-90847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024016-67617.gif)
(3)(理科)推广的结论为:若公差为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024009-46365.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024008-43506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024010-57439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024010-17599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024016-75887.gif)
则该数列的前
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024017-38234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024017-75216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024017-48615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-35155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-50606.gif)
对正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-37137.gif)
1
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-78185.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-80479.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024019-93633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-50606.gif)
2
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-78185.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024019-37274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024019-75348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024019-65892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024020-36259.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024020-58436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024020-56740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024020-40210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024020-75959.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024021-24710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024021-59922.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024021-23995.gif)
这表明对
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024020-58436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-50606.gif)
根据1
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-78185.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-78185.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024021-49814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024018-50606.gif)
利用以上结论,问题解法如下:
由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024015-63777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-29711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024015-81543.gif)
则利用探究结论可得:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024021-23699.gif)
不利用以上结论,解法如下:
由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024022-95538.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024013-27522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-67970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-29711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024014-48036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024022-21283.gif)
代入①可得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024022-66370.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024022-72998.gif)
核心考点
试题【(理)已知等差数列的公差是,是该数列的前项和.(1)试用表示,其中、均为正整数;(2)利用(1)的结论求解:“已知,求”;(3)若数列前项的和分别为,试将问题(】;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/20191013/20191013023959-92582.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-20145.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-76992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-37901.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-37920.gif)
(2)利用(1)的结论求解:“已知
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-77575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-83382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-70893.gif)
(3)若各项均为正数的等比数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-18569.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-34866.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-37901.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-76992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-72522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023959-77575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-83382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-11735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-65222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013024000-53810.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023941-84895.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023942-88284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023942-83541.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023942-77981.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023942-68639.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023924-83812.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023924-85448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023925-58710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023925-43940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023925-50257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023925-35217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023925-36586.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023926-82814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023924-83812.gif)
已知等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-35075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-59008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-35075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-54612.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-61170.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023916-39702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-61170.gif)
(Ⅱ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023916-65854.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-35075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023915-54612.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023916-95023.gif)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023910-82589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023910-66253.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023910-69664.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023910-83144.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023911-62969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023911-72667.gif)
(Ⅲ)在(Ⅱ)的条件下证明
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013023911-10392.gif)
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