1 . 已知数列
满足
,
.
(1)判断数列
是否是等比数列?若是,给出证明;否则,请说明理由;
(2)若数列
的前10项和为361,记
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec58977b75d78a7783de538705c1893.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cad972f22a1cb756fd9527d6a265be.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/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
2023-09-21更新
|
826次组卷
|
5卷引用:福建省厦门第一中学海沧校区2024届高三上学期9月月考数学试题
福建省厦门第一中学海沧校区2024届高三上学期9月月考数学试题福建省宁德第一中学2023-2024学年高二上学期10月学科素养数学试题(已下线)第五章 数 列 专题3 数列中的不等式能成立证明(已下线)专题10 数列不等式的放缩问题 (练习)(已下线)微专题1 数列综合应用-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)
名校
解题方法
2 . 已知正项数列
满足:对任意正整数
,都有
成等差数列,
成等比数列,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e719bd380ea9dd3ec2a20242bdf6380.png)
(1)求证:数列
是等差数列;
(2)设数列
的前项和为
,如果对任意正整数
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0197eeeeaafec6b1fdd7bb8509572f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a20dfd9c14d834c66b2070c41f66eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b55761181faa05961286eedfebca4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e719bd380ea9dd3ec2a20242bdf6380.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4f93dca4192c87d1ac77a2456bf12e.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b01041691ad489f126f05c18ea8f0fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd0dc83494c84b81687cf8c38736b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-01-25更新
|
437次组卷
|
3卷引用:福建省泉州市第一中学2024届高三上学期12月月考数学试题
名校
解题方法
3 . 已知数列
的前n项和为
,
,且
.
(1)求证:数列
为等差数列;
(2)已知等差数列
满足
,其前9项和为63.令
,设数列
的前n项和为
,求证:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc726d4282585efb91f8c34f5fd5cead.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
(2)已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d9bd40057948c5e3eb23064a673284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347bbb4dc9eaf978094e8bb89d41c56d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5608d0c8d3b5b997012cb6dc698d9f4.png)
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2024-01-12更新
|
997次组卷
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2卷引用:福建省德化一中、永安一中、漳平一中三校协作2024届高三上学期12月联考数学试题
名校
解题方法
4 . 已知数列
前
项和为
,且满足
.
(1)求数列
的通项公式;
(2)设
,求证:
.
![](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/c50e80d901052c78384e398765e61861.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7d039261709d9fa2b8ffcb0029eb2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc8c7b6a2c391b291e1445f309cad3f.png)
您最近一年使用:0次
2023-12-20更新
|
758次组卷
|
3卷引用:福建省莆田市第四中学2024届高三上学期第三次月考数学试题
福建省莆田市第四中学2024届高三上学期第三次月考数学试题云南省曲靖市师宗平高学校2023-2024学年高二上学期12月月考数学试题(已下线)重难点5-2 数列前n项和的求法(8题型+满分技巧+限时检测)
5 . 已知数列
的前
项和
,数列
满足:
.
(1)证明:
是等比数列;
(2)设数列
的前
项和为
,且
,求
;
(3)设数列
满足:
.证明:
.
![](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/5886e031a95a8d52c9306e6b1c518abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f2ecc6870129d1b5fa7f97b0824b83.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921439ba032dd3fdec48755411b04533.png)
(2)设数列
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ec3b51bbda2de5b7a2e0360c8adc46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8eb0aeb50edc4bfa079dc925aade88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cbe03ddf8f76a8d983ad63277ea2a3.png)
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2024-02-04更新
|
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4卷引用:福建省莆田第二中学2023-2024学年高二下学期3月月考数学试卷
福建省莆田第二中学2023-2024学年高二下学期3月月考数学试卷福建省福州第一中学2023-2024学年高二上学期第二学段模块考试数学试卷(已下线)江苏省南通市2024届高三第二次调研测试数学试题变式题 16-19(已下线)江苏省泰州市2024届高三第二次调研测试数学试题变式题16-19
名校
解题方法
6 . 已知数列
的前
项和为
.
(1)求数列
的通项公式;
(2)设
,数列
的前
项和为
,证明:
.
![](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/8edaca6cb49c0d403181fd35d889cdb4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff6d3c749cbe9072a47ce4152df19c.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/c1056f02e4a7e9b8fd479519eec2d9b3.png)
您最近一年使用:0次
名校
解题方法
7 . 已知
为数列
的前
项和,且
,
,
.
(1)证明:数列
为等差数列,并求
的通项公式;
(2)若
,设数列
的前
项和为
,求
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684d66f4e63d8b9518ff87fd1627fdc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d005409790b3192705a181b2c8e7dfed.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-12-20更新
|
1010次组卷
|
2卷引用:福建省莆田市锦江中学2023-2024学年高二上学期第二次月考数学试题
8 . 在数列
中,
,
的前
项为
.
(1)求证:
为等差数列,并求
的通项公式;
(2)当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a0a484cf87cb3bd96c3db9736c6f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62aadbfe3ef08851f220c3371684a1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb34ab1175fd4f7a8336221e559a784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2023-08-27更新
|
1874次组卷
|
7卷引用:福建省华安县第一中学2024届高三上学期10月月考数学试题
名校
解题方法
9 . 设
为数列
的前
项和,
.
(1)求数列
的通项公式;
(2)设
,证明:
.
![](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/eb4487d7daca378b322a42a8d04f341b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f770c2751f5f81c9b4419e4e99d1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a051cd30dd080d1a1a22b46b6444ae9.png)
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2023-12-29更新
|
2434次组卷
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8卷引用:福建省百校联考2024届高三上学期12月月考数学试题
福建省百校联考2024届高三上学期12月月考数学试题河北省金科大联考2024届高三上学期12月月考数学试题山东省德州市第一中学2024届高三上学期期末数学试题(已下线)考点12 数列中的不等关系 2024届高考数学考点总动员江西省宜春市宜丰中学2024届高三上学期期末数学试题(已下线)重难点5-2 数列前n项和的求法(8题型+满分技巧+限时检测)河北省衡水市枣强中学2024届高三上学期期末考试数学试题河北省衡水市深州中学2024届高三上学期期末考试数学试题
名校
解题方法
10 . 正数数列
满足
,且
成等差数列,
成等比数列.
(1)求
的通项公式;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38531760ffe5777683041e8ef2d2cede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a20dfd9c14d834c66b2070c41f66eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b55761181faa05961286eedfebca4f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fc21d3913caa9495d33535694e52a3.png)
您最近一年使用:0次
2023-08-01更新
|
922次组卷
|
4卷引用:福建省宁德市古田县第一中学2023-2024学年高二上学期第一次月考数学试题
福建省宁德市古田县第一中学2023-2024学年高二上学期第一次月考数学试题广东省广州大学附属中学等三校2022-2023学年高二下学期期末联考数学试题湖南省长沙市周南中学2023-2024学年高三上学期入学考试数学试题(已下线)特训02 期末解答题汇编(第1-5章,精选38道)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)