1 . 已知数列
满足
,
,
,若数列
的前
项和为
,则所有满足
的
的和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4123422b5a6621da6a3214aa8c3e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a97aa79f9746d819f37958c3f240965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4a9144e09f88e420731038354d5202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.875 | B.918 | C.994 | D.1015 |
您最近一年使用:0次
2024-05-19更新
|
199次组卷
|
3卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷 江西省南昌市安义中学2023-2024学年高二下学期4月期中调研测试数学试题(已下线)4.3.2等比数列的前n项和公式(2)
名校
2 . 已知圆心在
轴正半轴上的一系列相外切的圆的圆心的坐标为
,且满足
,第
个圆的圆心横坐标为
,这
个圆的面积之比为
,第1个圆的半径为1.记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19af21827ffd49c3842e1443244940e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e684bbf8039dc14ea6a402f3478b3aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702de74c38885954ec1fff041b0c2f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f933f2a8c0a6a2a2903a071c18c9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19af21827ffd49c3842e1443244940e.png)
您最近一年使用:0次
3 . 已知等差数列
和等差数列
的前
项和分别为
,
,
,
.
(1)求数列
和数列
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6403597ee5c99469e6053ae566a9469.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00147ca04fe49733ef62237fd4c3ecd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
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解题方法
4 . 北宋数学家沈括博学多才、善于观察.据说有一天,他走进一家酒馆,看见一层层垒起的酒坛,不禁想到:“怎么求这些酒坛的总数呢?”,沈括“用刍童(长方台)法求之,常失于数少”,他想堆积的酒坛、棋子等虽然看起来像实体,但中间是有空隙的,应该把他们看成离散的量.经过反复尝试,沈括提出对上底有ab个,下底有cd个,共n层的堆积物(如图),可以用公式
求出物体的总数.这就是所谓的“隙积术”,相当于求数列ab,
的和,“隙积术”给出了二阶等差数列的一个求和公式.现已知数列
为二阶等差数列,其通项
,其前n项和为
,数列
的前n和为
,且满足
.
(1)求数列
的前n项和
;
(2)记
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea2d05ec2ace95c566eacfbc721c647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0ada0c24b4f4a74ba37968a910f02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62cd56c9d7b7865d8c145a8e74c7c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d1b5d9c88470aed5e224b8109a6835.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/81afd846-70ff-4fd5-86cd-b457ff6c93ab.png?resizew=177)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229fa99b3fbfcd20137a53f8db5117c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bd7d18f67e90a7c37fad4252e43c9d.png)
您最近一年使用:0次
名校
5 . 数列
的通项公式为
,前
项和为
,下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d769bccbcfe1458ef7e63d1c2af451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() ![]() |
B.存在正整数![]() ![]() |
C.存在正整数![]() ![]() |
D.记![]() ![]() |
您最近一年使用:0次
解题方法
6 . 已知数列
的前
项和为
,
,且
.
(1)求
的通项公式;
(2)设
,
为数列
的前
项和,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73af653d11c3d6c2673300a6622a5279.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4db39a76614ea6d8207f445f8b8622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029da2067b3564cee13879e402a89a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe667f4e2162221b6e4f2796c1ccd39.png)
您最近一年使用:0次
名校
7 . 记
为数列
的前n项和,已知
,
,数列
满足:
,且
.
(1)求数列
的通项公式;
(2)令
,求数列
的前n项和
的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911c88654ea7669c5e54542b0f16d89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50a454957acee6310d508674aa8b300.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef0cb445c3cd097581c35e2b40750a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-11-07更新
|
1999次组卷
|
2卷引用:单元测试B卷——第四章 数列
8 . 已知数列
满足
且
的前
项和为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8733f412a72beab3396a77633e54b17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2bfd1bccf86167d165f06c6c888a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-09-07更新
|
493次组卷
|
2卷引用:广东省佛山市南海区九江中学2023-2024学年高二下学期4月月考数学试题
名校
解题方法
9 . 已知数列
中
,关于
的函数
有唯一零点,记
.
(1)判断函数
的奇偶性并证明;
(2)求
;
(3)求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f4d4fa1b049045d58a9571a0709004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072010cccaa77474c07b66816ce4ae92.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f4d4fa1b049045d58a9571a0709004.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f8c399c162dbd37d2aa304a4a3a1fd.png)
您最近一年使用:0次
10 . 记
为数列
的前
项和,已知
的等差中项为
.
(1)求证
为等比数列;
(2)数列
的前
项和为
,是否存在整数
满足
?若存在求
,否则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688bdce2ea7b68d3471521059527dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a080c94bf1ffea8d5af10f9688978fb5.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46093d4801ed07e6ac2814c5ab838df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0304444b3dcd3e44f3004f5f98c844a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次