题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155937-80818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-69247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-54432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-30430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-89901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155939-25037.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-69247.png)
(2)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155939-29495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155939-60559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155939-29495.png)
(3)在满足(2)的条件下,求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155939-97906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-54432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155940-93059.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155940-63238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155940-70384.png)
解析
试题分析:(1)利用
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155940-68315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155941-74146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155941-28285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155941-90704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155941-46853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155942-92035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155942-91771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155942-43585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155942-43585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155940-93059.png)
试题解析:(1)证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155942-74446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155943-57331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155943-11534.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155943-24080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155943-98563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155944-73371.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155939-25037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155944-49126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155944-53913.png)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155944-67890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155944-42114.png)
(2)解:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155945-33519.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155941-90704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155945-48708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155945-11362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155945-77951.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155941-46853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155942-92035.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155945-69139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155940-63238.png)
(3)解:由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155946-91264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155946-92989.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155946-88635.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-54432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155946-51823.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155947-90895.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155947-81694.png)
①-②得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155947-15062.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155947-61280.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155948-50009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155948-79209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155948-79565.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155948-40714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155949-26062.png)
③-④得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155949-71601.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155949-32486.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155949-59647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155950-46047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155950-79817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155950-61182.png)
12分
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155938-54432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155950-60127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155950-78380.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155951-34553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155951-99254.png)
法二:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155951-32294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155952-92443.png)
9分
①-②得:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155952-41369.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155952-55813.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155952-41152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155953-42731.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155953-33765.png)
核心考点
试题【设为数列的前项和,对任意的,都有(为正常数).(1)求证:数列是等比数列;(2)数列满足求数列的通项公式;(3)在满足(2)的条件下,求数列的前项和.】;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/20191009/20191009155905-29199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155905-70142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155906-46415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155906-29057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155906-24437.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155906-17030.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155905-29199.png)
(3)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155907-11001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155906-46415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155907-76963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155907-15731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155906-46415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155907-81079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155421-86475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155422-20617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155422-83097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155422-22877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155422-35425.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155421-86475.png)
(2)若数列满足
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155422-92663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155423-70339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155422-20617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155423-36294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155149-87699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155149-85920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155149-21707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155149-51509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155150-22710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155150-97210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155150-10129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155009-34991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155010-72849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155010-97128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155010-67918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155010-42849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155010-34242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155011-73288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155010-67918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155011-55779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155011-10136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155011-10136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155011-35681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155011-79459.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155012-74341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155011-79459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155009-34991.png)
(2)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155012-50199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155012-57020.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155012-83070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155013-18627.png)
②记数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155009-34991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155013-19898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155013-88816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155013-18627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155013-52565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009155013-18627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009154446-40350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009154447-65474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009154447-70768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009154447-18359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009154447-38950.png)
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