解题方法
1 . 已知函数
,
,数列
是各项均不为0的等差数列,点
在函数
的图像上,数列
满足
,
,且
(
),
(1)求数列
的通项公式,并证明数列
是等比数列;
(2)若数列
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f47ce72c592e5dab3590d6d0475096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a64286dec61958bc6d396d8d500a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938cbb985e51f5053e82c2861870433b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bb97b3eaf923069c70fb221ebb919b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fae8221de1b787ee399d6e345a152f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921439ba032dd3fdec48755411b04533.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9737bbebe8ff3f39b662ee441f57ef2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20afcac0bb1565b8deaed39c2b15cd4.png)
您最近一年使用:0次
2 . 数列
是等差数列,
是公比为
的等比数列,
是
的前
项和,已知
,
.
(1)求
的值;
(2)证明:将
按适当顺序排列后,可以成等差数列.
![](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/9aa8a716a31b0f51b70fdf9bdb257909.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3d772eda3f0d489a5bc40ab501c35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5a36de2febe3a199198f33e5b92fdb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)证明:将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca88d734fb81ff9dc6825defd2622fd.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
的前
项和为
, 且
, __________.请在
成等比数列;
, 这三个条件中任选一个补充在上面题干中, 并解答下面问题.
(1)求数列
的通项公式;
(2)设数列
的前
项和
, 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751c3b0c7d916ddc24d7bd036ea0eecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4011c597ba394120a1a74b6f4a401159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25108967f8f95c445c109348592d4fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3432f48e3f2e684d45e89403110ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9694346716bad8031f17fff37273ddc.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751c3b0c7d916ddc24d7bd036ea0eecd.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55f3cadcc65d380f74102037b46a4f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59887a5ab83d604d78b8a204b7f88bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24974f2d84f24c6dc2d836e0d9fa5359.png)
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2022-12-26更新
|
849次组卷
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7卷引用:四川省南充市2021-2022学年高三高考适应性考试(一诊)数学(理)试题
四川省南充市2021-2022学年高三高考适应性考试(一诊)数学(理)试题(已下线)热点07 数列与不等式-2022年高考数学【热点·重点·难点】专练(新高考专用)湖南省岳阳市2022届高三下学期教学质量监测(三)数学试题四川省遂宁市第二中学校2023届高三上学期一诊模拟考试理科数学试卷(二)(已下线)数列求和广东省揭阳市普宁国贤学校2022-2023学年高二上学期期末数学试题山西省晋城市泽州县晋城一中教育集团南岭爱物学校2022-2023学年高二上学期1月期末调研考试数学试题
名校
解题方法
4 . 已知等差数列
中,
,
.
(1)求数列
的通项公式.
(2)记数列
的前
项和为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117dd04afc6d1a34828c7f9da7663a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d3c3f8e2e4003eefda164fb11c1444.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](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/0031136b88c5c677de5ab4b3c74b7388.png)
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2023-03-08更新
|
597次组卷
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13卷引用:拓展二 数列求和的方法(精练)-2020-2021学年一隅三反系列之高二数学新教材选择性必修第二册(人教A版)
(已下线)拓展二 数列求和的方法(精练)-2020-2021学年一隅三反系列之高二数学新教材选择性必修第二册(人教A版)四川省绵阳第一中学2021届高三一诊适应性考试数学(理)试题金科大联考2020届高三5月质量检测数学(文科)试题安徽省皖北名校2020-2021学年高二上学期第一次联考数学试题河南省豫西名校2020-2021学年高二10月联考数学试题(已下线)第六单元 数列(B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷河南省洛阳市豫西名校2020-2021学年第一次联考高二数学试题陕西省宝鸡市教育联盟2020-2021学年高三上学期第二次月考理科数学试题陕西省宝鸡市教育联盟2020-2021学年高三上学期第二次月考文科数学试题(已下线)专题6-2 数列求和15种类型归纳-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)陕西省西安交通大学第二附属中学(南校区)2020-2021学年高三上学期10月月考理科数学试题河南省豫西名校2022-2023学年高二上学期第一次联考数学试题青海省西宁市大通县第一中学2024届高三第二次月考数学文科试题
名校
解题方法
5 . 已知数列
为等差数列,
是数列
的前
项和,且
,
,数列
满足
.
(1)求数列
、
的通项公式;
(2)令
,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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fcd86b9ed6819116a261629f96fae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cf0e722239dd3c7f44795f74aa6bf4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1796d3b3d59e53a318ced796ebda0538.png)
您最近一年使用:0次
2023-01-18更新
|
762次组卷
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5卷引用:安徽省皖江名校联盟2021-2022学年高三上学期第四次联考理科数学试题
6 . 已知数列
为等差数列,数列
为等比数列,且
,
,
,
.
(1)求
,
的通项公式.
(2)已知
,求数列
的前2n项和
.
(3)求证:
.
![](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/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f81b63fc0cffb75cc6aeae64591277c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a72a928a6bcde50c7e502669880892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c72dc9034f1aca2b4ef5afb4475c66.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd37f8bb8b52db13ba5c48b878de23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5e7f98ec8f4ea9b9492405094c5380.png)
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2022-12-15更新
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1747次组卷
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6卷引用:天津市静海区第一中学2021-2022学年高三上学期第四次阶段检测数学试题
7 . 已知等差数列
的前n项和为
,数列
是各项均为正数的等比数列,
,
.
(1)求数列
和
的通项公式;
(2)令
,求数列
的前n项和
;
(3)令
,数列
的前n项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e79e4498b00abf4d9aabdc4d2f2bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f1f1fd8717203ae837d22aaf7f8361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e9b495d5b1619e6ed0912516ed86d7.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7554176f48d9f042d96ec5a9e01f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733969643c55ec0ddfddd781a6545778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529538fd39fe317bd6cfe8e07fe3c998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477b1f17dd05c7c1878fc8345e3abf57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea2ec890c55ef68d69d9c9d9df5e9fe.png)
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2022-10-24更新
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3卷引用:天津市四校(杨柳青一中、咸水沽一中 、四十七中,一百中学)2020-2021学年高二上学期期末联考数学试题
名校
解题方法
8 . 已知数列{an}(n∈N*)是公差不为0的等差数列,a1=1,且
,
,
成等比数列.
(1)求数列{an}的通项公式;
(2)设数列{
}的前n项和为Tn,求证:Tn<1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14771ad8f9fd441429ba43bf00ec794e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab0ddb0876fafbfb4dd8451f8b38c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221e08845f95c15b3ee8a64fc80ce234.png)
(1)求数列{an}的通项公式;
(2)设数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0d9f8bf8dd91d8cd659ce6fb9c80b8.png)
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2022-10-20更新
|
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2卷引用:江苏省连云港市灌南高级中学2021-2022学年高二上学期期中数学试题
解题方法
9 . 已知数列
是公差d不等于0的等差数列,且
是等比数列,其中
.
(1)求
的值.
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec07a126ada2c921c5b4337f77854cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9dbae694b72b50409733bce52398b83.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373ecb5531c1593f13a0ed081597b3cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b653cc33c01873e1105a74a21d47dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2685c6c2ee7d0cfdd8ebef4c6ee43852.png)
您最近一年使用:0次
名校
解题方法
10 . (1)已知在递增的等差数列
中,
.求
的通项公式;
(2)已知数列
中,
.证明:数列
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f8540049a5936f22fcdd50d1c25fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38356321dfd19c60a8b1938618deb089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
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2022-11-18更新
|
836次组卷
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2卷引用:湖南省株洲市第八中学2021-2022学年高二上学期期中数学试题