1 . 已知数列
满足
=
且
=
-
(![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b0aafc603ba02b6702e785b00a5013.png)
).
(1)证明:1
(![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b0aafc603ba02b6702e785b00a5013.png)
);
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deda1cd6fa436beb194738f75ee1650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b0aafc603ba02b6702e785b00a5013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
(1)证明:1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e587190974891f34f5efd34fad666ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b0aafc603ba02b6702e785b00a5013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
(2)设数列的前
项和为
,证明
(
).
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19卷引用:2015年全国普通高等学校招生统一考试理科数学(浙江卷)
2015年全国普通高等学校招生统一考试理科数学(浙江卷)(已下线)专题09 数列与数学归纳法-2021年浙江省高考数学命题规律大揭秘【学科网名师堂】人教版高中数学 高三二轮 专题14 数列求和及综合应用 测试(已下线)2018年5月9日 证明不等式的基本方法——《每日一题》2017-2018学年高二文科数学人教选修4-5(已下线)2018年9月25日 《每日一题》人教必修5-不等关系与不等式(2)(已下线)2018年10月22日 《每日一题》人教必修5--数列与不等式的综合(上学期期中复习)【全国百强校】黑龙江省双鸭山市第一中学2018-2019学年高一下学期期中考试数学(理)试题(已下线)2019年9月24日 《每日一题》必修5—— 不等关系与不等式(2)沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第四章 数列与数学归纳法高考题选(已下线)第26讲 数列求和及数列的综合应用-2021年新高考数学一轮专题复习(新高考专版)(已下线)专题05 数列-十年(2012-2021)高考数学真题分项汇编(浙江专用)(已下线)专题28 证明不等式的常见技巧-学会解题之高三数学万能解题模板【2022版】(已下线)4.1数列的概念B卷(已下线)第三篇 数列、排列与组合 专题5 迭代数列与极限 微点4 Stolz公式背景下的数列题(已下线)第三篇 数列、排列与组合 专题5 迭代数列与极限 微点5 迭代数列与蛛网图(已下线)专题11 数列前n项和的求法 微点5 裂项相消法求和(三)(已下线)专题14 类等差法和类等比法 微点1 类等差法和类等比法的主要类型(已下线)专题21 数列解答题(理科)-3专题28数列解答题
2 . 已知数列
(
,
)满足
,
,其中
,
.
(1)当
时,求
关于
的表达式,并求
的取值范围;
(2)设集合
.
①若
,
,求证:
;
②是否存在实数
,
,使
,
,
都属于
?若存在,请求出实数
,
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92676454db896b3761333fe2717bce03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8572a331f30d2b31f8a789a66d0e565c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f4a16760b47e0c3188445c426c5005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f4a16760b47e0c3188445c426c5005.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5646880d6380783634c68d2ddbee2e15.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd82b5223c2a708c1729db2a3750990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70792383ff1c955255afe70b7c9c90c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08048db0a4115538251553b85da3ddfb.png)
②是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd8a2fbb8ed23a0d23f293b9edb04a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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1289次组卷
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3卷引用:2015届浙江省高三第二次考试五校联考理科数学试卷
3 . 在单调递增数列
中,
,
,且
成等差数列,
成等比数列,
.
(Ⅰ)(ⅰ)求证:数列
为等差数列;
(ⅱ)求数列
的通项公式.
(Ⅱ)设数列
的前
项和为
,证明:
,
.
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/2e08acc48f0b40a7abfbf10ed8d4d220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/d38e3a4322944de5936679c72b227012.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/f35a59c609cc4c278ae6c6645c0a57b8.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/72eabbe954064aa1b973914c8c6fa9e9.png)
(Ⅰ)(ⅰ)求证:数列
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/922fea699deb4280823895b67427f330.png)
(ⅱ)求数列
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/88ebdecc57164f0eab66aa81e99d806c.png)
(Ⅱ)设数列
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/7243d64298aa4093901dc98a222e9e09.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/0e02509405e648109c87a89024b7d7e1.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/41667ac835a14e6fa4cea0838d4d86f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19c066f405598229b8123ae152df314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
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4 . 已知函数
,数列
的前
项的和为
,点
均在函数
的图象上.
(1)求数列
的通项公式
;
(2)令
,证明:
.
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/a98ed18f74fc4c00b9c79fbb288cdbad.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/4825e46895af49379b53b3afbabdf529.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/2de9e23210d14b98bdcd0ea2813614fb.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/38a42d81e8c54de98267abf94371dfa5.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/3c7a2f20b39a42bc88b91bb2682da22b.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/892578fddbb447748df0ad1ce76d1086.png)
(1)求数列
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/4825e46895af49379b53b3afbabdf529.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/3f82c0f4d478433f88759932cf66333b.png)
(2)令
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/a26f3d0d8d9d4ef7a17e3e036c3ff0dd.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571963023196160/1571963029110784/STEM/9ce2e0ef57be40119123015402dd0682.png)
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14-15高三上·浙江温州·期中
名校
解题方法
5 . 已知函数
.
(1)若函数
为偶函数,求
的值;
(2)若
,求函数
的单调递增区间;
(3)当
时,若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66727de73bdb89a3cce558372ca7301.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b916c6d3fb2fdc67421489f207c93903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c989623de36d03965b327d2e49c31b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2016-12-03更新
|
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|
5卷引用:2015届浙江省温州市十校联合体高三上学期期中联考理科数学试卷
真题
名校
6 . 给定常数
,定义函数
,数列
满足
.
(1)若
,求
及
;
(2)求证:对任意
,;
(3)是否存在
,使得
成等差数列?若存在,求出所有这样的
,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4950cc100c4f08bec9fc33ce6ddedac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69bd34a73127f3483a9d50d2dc1755c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8613ce827804b9485d8dfc0ca2d563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d043d6b72ab55699dcbb12cfc242b006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922de166bb11f7828ca5496015ca97fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ebe11bc5d30b80341cc3be681d58a.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c01bd7853f3d558f5b34c8decb1124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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8卷引用:2013年全国普通高等学校招生统一考试理科数学(上海卷)
2013年全国普通高等学校招生统一考试理科数学(上海卷)上海市金山中学2016-2017学年高一下学期期末数学试题沪教版(上海) 高二第一学期 新高考辅导与训练 第7章 数列与数学归纳法 7.2(2)等差数列的定义与通项公式的应用沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第四章 数列与数学归纳法高考题选 浙江省杭州学军中学2023-2024学年高二下学期6月月考数学试题(已下线)考向14 等差数列-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)第08讲 等差、等比数列-2(已下线)4.1等差数列及其通项公式(第1课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件