1 . 已知数列
的前n项和为
,且
,
(
).
(1)证明
是等比数列,并求
的通项公式;
(2)若
,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/28b69fa8e4172018faebfa39782626e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483eb4433fee05a5810a276433b1742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6fd7a169fb7e25a0f0efe4460b68c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
2 . 在数列
中,若存在常数
,使得
恒成立,则称数列
为“
数列”.
(1)若
,试判断数列
是否为“
数列”,请说明理由;
(2)若数列
为“
数列”,且
,数列
为等比数列,且
,求数列
的通项公式;
(3)若正项数列
为“
数列”,且
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8158441521b4c35044b2c27b0df96d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075f4a124ee7f174909a106a94f5ad42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196c99381f37d23ce5c7ba450d98330b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb4bba6777941fbf01de6094c3ff21d.png)
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5卷引用:河北省百师联盟2024届高三下学期开学摸底联考数学试题
真题
名校
3 . 已知
是等差数列,
.
(1)求
的通项公式和
.
(2)设
是等比数列,且对任意的
,当
时,则
,
(Ⅰ)当
时,求证:
;
(Ⅱ)求
的通项公式及前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35e133418e9dbd8f81528b4b7ff9c25.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e8e5b901d8f8a8b6ec7740f1b55ed4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6bc55d5eb2c3d085b62ffcd8d138d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2daddb01510526b8fa639b18635e986d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e7d5ea07ebd45f587cbab2b3fd77ba.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99380bd8acd91cb1ffbd49e896d34f1d.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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|
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23卷引用:河北省邢台市邢台部分高中2024届高三上学期11月期中数学试题
河北省邢台市邢台部分高中2024届高三上学期11月期中数学试题2023年天津高考数学真题(已下线)专题7 等比数列的性质 微点2 等比数列前n项和的性质专题05数列(成品)(已下线)专题15 数列不等式的证明 微点1 反证法证明数列不等式(已下线)专题11 数列前n项和的求法 微点1 公式法求和(已下线)2023年天津高考数学真题变式题16-20江苏省淮阴中学等四校2023-2024学年高三上学期期初联考数学试题(已下线)第05讲 数列求和(练习)宁夏银川市第二中学2023-2024学年高二上学期月考二数学试卷(已下线)等差数列与等比数列(已下线)第3讲:数列中的不等问题【练】(已下线)重难点03:数列近3年高考真题赏析-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)专题6.2 等比数列及其前n项和【十大题型】(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)专题30 等比数列通项与前n项和(已下线)专题21 数列解答题(文科)-3(已下线)专题21 数列解答题(理科)-3安徽省六安第一中学2024届高三适应性考试数学试题专题06数列专题11数列(已下线)三年天津专题09数列(已下线)五年天津专题09数列
4 . 已知数列
的首项
,且满足
.
(1)求证:数列
为等比数列;
(2)若
,数列
前
项的和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ebcef1b552c3dbac4b69ec9acdf580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ec25765644525842cef1002e24f0ee.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2823ff24bf2fb0ef7b7a15355624ead4.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/08eb71ecf8d733b6932f4680874dbbf3.png)
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5卷引用:河北省石家庄市辛集市2022-2023学年高二下学期期末数学试题
河北省石家庄市辛集市2022-2023学年高二下学期期末数学试题湖南省怀化市2022-2023学年高二上学期期末数学试题(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题17-22湖南省邵阳市新邵县2023-2024学年高二上学期期末数学试题(已下线)专题01 数列(6大考点经典基础练+优选提升练)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)
5 . 在数列
中,
,且
.
(1)证明:
,
都是等比数列;
(2)求
的通项公式;
(3)若
,求数列
的前n项和
,并比较
与
的大小;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67e613e9a56e7aae7fed0f7d0ab199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25210e080f01c3e6ffdb55ee546b474d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea93612158b3d9b4d591d21ce628a68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7553d64dee43f97d1e16e71b92d96f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b17093f6e7fac55426336f242d87101.png)
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名校
解题方法
6 . 已知数列
满足
,
,
,n为正整数.
(1)证明:数列
是等比数列,并求通项公式;
(2)证明:数列
中的任意三项
,
,
都不成等差数列;
(3)若关于正整数n的不等式
的解集中有且仅有三个元素,求实数m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/c4ceb3142d785fe846a8935df2e45500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d280d7c7637028f59649b3025e553cb7.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86177a9ae8baa220750bf7c7f2f41eae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ac33c2fdec7345569781f9e5f6227d.png)
(3)若关于正整数n的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18f925d1944df03865d6c45d2cdd130.png)
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2022-01-22更新
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550次组卷
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7 . 已知数列
,
满足
,
,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
(1)求
,
的值,并证明数列
是等比数列;
(2)求数列
,
的通项公式.
![](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/ce17bcde98a2af9d80e09bfe16327eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9108044423b482373d7c95bdf172021c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec12a9a60f82467bf7bf834a9a9b1f7.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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名校
8 . 已知数列
满足
,
,数列
满足
,
,对任意
都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b02b3a89627300dc178e34c0103639.png)
(1)求数列
、
的通项公式;
(2)令
.求证:
.
![](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/c624ff1743d90a1bdc59a095bfdd898e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5007cf5afb87e8f4667438d7e3ce88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b02b3a89627300dc178e34c0103639.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4ed9d2c4f561c118ad7581fda564bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3853475e5d5310e0b325de06c55116c9.png)
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2019-12-23更新
|
280次组卷
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2卷引用:河北省张家口市宣化一中2019-2020学年高一上学期12月月考数学试题
9 . 已知数列
满足
,
.
(Ⅰ)证明:
是等比数列;
(Ⅱ)证明:数列
中的任意三项不为等差数列;
(Ⅲ)证明:
.
![](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/f3cfc11343590efb61c88b627f479be9.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098d9e65e9676e4386c5d861c8eb03b5.png)
(Ⅱ)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(Ⅲ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6257827fd179f2f03f23d5a9f75bc0.png)
您最近一年使用:0次
10 . 已知数列
满足:
,且
.
(1)求证:数列
是等比数列;
(2)设
是数列
的前
项和,若
对任意
都成立.试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2d19d6b259f57f4659e8643e02a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c044e907c418159ff0b98c5fea4dc748.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](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/a0823d78ca3873c8a070208d54cf716b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2017-06-20更新
|
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