名校
解题方法
1 . 公比为
的等比数列
的前
项和
.
(1)求
与
的值;
(2)若
,记数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.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/e6b981758450e9dcee6cfbe6c67c61f8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f5b1a6c081ca11ee5c4723525a43ce.png)
您最近一年使用:0次
2024-01-16更新
|
1320次组卷
|
3卷引用:广东省潮州市2024届高三上学期期末数学试题
名校
解题方法
2 . 已知数列
的前n项和为
,且
.
(1)求证:
是等比数列;
(2)在
与
之间插入n个数,使这
个数组成一个公差为
的等差数列,求数列
的前n项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e9b907c54b9b76f3a6d3a9fa56d8ea.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f774872ffec6c34cadeb450cfefdb11e.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0526bcbb60d5258b461ab634e913212d.png)
您最近一年使用:0次
2023-02-23更新
|
1004次组卷
|
2卷引用:天津市七区2022-2023学年高二上学期期末数学试题
3 . 已知公差不为零的等差数列
的前n项和为
,
,
,
,
成等比数列,数列
的前n项和
.
(1)求数列
和
通项公式;
(2)求
的值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36183db0759eec0e108274d229fcd00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163d7c4a5263414c45603254e60afe13.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9c5080960098a1799d0eb23e976b3c.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e930426d9c32f1cf4a8ace703fe2dbec.png)
您最近一年使用:0次
解题方法
4 . 已知数列
的前n项和为
,数列
的前n项和为
,从下面①②③中选择两个作为条件,证明另外一个成立.①
,②
,③
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f6fba55664fcee2a89ce3e76d4c5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128d43fbfe37d2334f8666239efc7e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdddc9047af28726f98bc82761407665.png)
您最近一年使用:0次
2022-07-21更新
|
299次组卷
|
4卷引用:辽宁省葫芦岛市2021-2022学年高二下学期期末数学试题
辽宁省葫芦岛市2021-2022学年高二下学期期末数学试题(已下线)模块五 专题3 全真拔高模拟(高二人教B)人教A版(2019) 选修第二册 数学奇书 第四章 数列 教考衔接(二)数列开放型问题(已下线)4.3等比数列(3)
名校
解题方法
5 . 已知数列
的前n项和为
,且
,
.
(1)证明:
为等比数列,并求
的通项公式;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14de5da0d1da50a29fc1e18f860b29ff.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-10-01更新
|
2071次组卷
|
9卷引用:吉林省辽源市田家炳高级中学校2022-2023学年高二上学期期末数学试题
吉林省辽源市田家炳高级中学校2022-2023学年高二上学期期末数学试题吉林省辽源市田家炳高中友好学校第七十四届2022-2023学年高二上学期期末联考数学试题河北省示范性高中2023届高三上学期第一次调研数学试题浙江省C8名校协作体2022-2023学年高三上学期第一次联考数学试题四川省隆昌市第七中学2022-2023学年高三上学期11月月考理科数学试题(已下线)4.3 等比数列(3)(已下线)第7讲 数列求和9种常见题型总结 (1)浙江省金华市曙光学校2023-2024学年高二上学期12月月考数学试题(已下线)4.3等比数列(3)
6 . 已知数列
的前
项和为
,满足
,
,
.
(1)证明:数列
是等比数列;
(2)记
,设
,求数列
的前
项和
.
![](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/b1549723d901eeb2cf966e322f404a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e1a9eec989e8233a81c8149a8991f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6417526489efc14858993d815ad8f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284ecbf2660e975927e51eb68bfc436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
您最近一年使用:0次
2022-05-13更新
|
1063次组卷
|
3卷引用:辽宁省锦州市2022-2023学年高三上学期期末考试数学试题
7 . 已知数列
中,其前
项和
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f20826a21f6f58bb90915099a84dbe3.png)
.
(1)求证:数列
为等比数列,并求
的通项公式;
(2)设
,求数列
的前项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e22d193eeea7dd2d61f54ea468be716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f20826a21f6f58bb90915099a84dbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866eee57f4f86f03d0d4fc8eb4b8a7f2.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90205cb00b7143a8dcdd2e4cb3f190b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0096ced57c6f31f2e0fe402bd56334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2021-11-26更新
|
594次组卷
|
2卷引用:黑龙江省八校2021-2022学年高三上学期期末联合考试数学(理)试题
8 . 已知数列{an}的前n项和为Sn,且Sn=2an
.
(1)证明:数列{an}是等比数列;
(2)设bn=(2n
)an,求数列{bn}的前n项和Tn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)证明:数列{an}是等比数列;
(2)设bn=(2n
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
您最近一年使用:0次
2021-10-04更新
|
652次组卷
|
8卷引用:福建省福州市2018届高三上学期期末质检数学(文)试题
福建省福州市2018届高三上学期期末质检数学(文)试题安徽省定远重点中学2019届高三上学期期末考试数学(文)试题【全国百强校】北京师大实验中学2019届高三3月份高考模拟文科数学试题四川省阆中中学2020-2021学年高三上学期开学考试数学(理)试题(已下线)专题04 数列求和(知识串讲)-2020-2021学年高二数学重难点手册(数列篇,人教A版2019选择性必修第二册)(已下线)第19节 数列求和江西省抚州市金溪县第一中学2023届高三上学期第二次月考数学(文)试题四川省成都市玉林中学2023-2024学年高二下学期4月诊断性评价数学试题
名校
解题方法
9 . 已知数列
的前n项和为
,且
.
(1)证明:数列
是等比数列;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add31cf3a48df4a45b0e76cb560b43a3.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf3da897eb73b729f66bb0d700775c5.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-03-03更新
|
631次组卷
|
4卷引用:河南省新乡市2021-2022学年高二上学期期末考试数学(文)试题
河南省新乡市2021-2022学年高二上学期期末考试数学(文)试题河南省新乡市2021-2022学年高二上学期期末考试数学(理)试题湖南省百所学校大联考2021-2022学年高二下学期入学考试数学试题(已下线)湖南省长沙市长郡中学2022届高三下学期月考(六)数学试题
名校
解题方法
10 . 已知数列
的前n项和为
,且
,
,数列
满足
.
(1)求数列
的通项公式;
(2)设
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131719ddba3ab35953e148446e55dec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8542eab3c53c9307d9e24354a21638f9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f22734c15f1ca7b2dbb38ba2f565db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.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/e672c3d231081d12e44a4211e5ac60bf.png)
您最近一年使用:0次
2021-05-29更新
|
919次组卷
|
5卷引用:江苏省镇江市扬中市第二高级中学2022-2023学年高二下学期期末检测数学试题
江苏省镇江市扬中市第二高级中学2022-2023学年高二下学期期末检测数学试题河南省周口市川汇区周口恒大中学2023-2024学年高二上学期期末数学试题江苏省徐州市2021届高三下学期高考考前模拟数学试题江苏省徐州市2021届高三下学期5月四模数学试题(已下线)一轮复习大题专练32—数列(证明不等式问题)-2022届高三数学一轮复习