解题方法
1 . 已知在
中,
成等差数列,则
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099c31a55ec44861d4c3cf8343d9024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b037d1372328b2e7f0db755ccc88c2.png)
您最近一年使用:0次
名校
2 . 正实数构成的集合
,定义
,且
.当集合
中的元素恰有
个数时,称集合A具有性质
.
(1)判断集合
是否具有性质
;
(2)设集合
具有性质
,若
中的所有元素能构成等差数列,求
的值;
(3)若集合A具有性质
,且
中的所有元素能构成等差数列.问:集合A中的元素个数是否存在最大值?若存在,求出该最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff9423a8ca3d361e6c2e306e85f645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca01ec02f3776fcd41abf91c11f00cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3aa0dd21599a617660672ea6410c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636c838e9c10d079e5df897fce90761b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d00b592b51981ec491c1a1275593143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f9d1bf24fb71dbec06d9728abde542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ee39cb5dda61782c6c0989fe5f8016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6276b807e05eebe754764c1fc29cb5d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
(3)若集合A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636c838e9c10d079e5df897fce90761b.png)
您最近一年使用:0次
2023-07-10更新
|
259次组卷
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3卷引用:【北京专用】专题03数列(第三部分)-高二上学期名校期末好题汇编
名校
3 . 已知
,等差数列
的前
项和为
,记
.
(1)求证:函数
的图像关于点
中心对称;
(2)若
、
、
是某三角形的三个内角,求
的取值范围;
(3)若
,求证:
.反之是否成立?并请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71de2abab31c4eb56f306f90dab97b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/5395b2d08fce7c50d6281ef406cfe4bf.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd4b78b52a322453c700b62660e6ca57.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c5f3a5c55e0c95191c5a893f63062.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4847cf7c0d99d9c83ca571bef8eefc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58b9a59084755c0a4781922cfa03ee5.png)
您最近一年使用:0次
2023-04-13更新
|
1036次组卷
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3卷引用:专题06 数列及其应用
名校
解题方法
4 . 在数列
中给定
,且函数
的导函数有唯一零点,函数
且
,则
( ).
![](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/ace9df07b6c1ac84e17712165b7519b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548d9db31a2a612be95df4240ceb3474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924507867f24d025d0ba1f6b46772cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-03-26更新
|
1345次组卷
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4卷引用:专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-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)
(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-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)湖北省武汉市华中师大一附中2023届高三下学期第二次学业质量评价检测数学试题黑龙江省双鸭山市第一中学2022-2023学年高二下学期期中数学试题湖南省郴州市宜章县多校2023届高三二模联考数学试题
名校
5 . 已知函数
,
,各项均不相等的数列
满足:
,令
.
(1)试举例说明存在不少于
项的数列
,使得
;
(2)若数列
的通项公式为
,证明:
对
恒成立;
(3)若数列
是等差数列,证明:
对
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40eb99ee3e13901131e3f8298249adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ffd2c4dae9a37f660e23ccea5ef320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c760bfcfc098d43c5bc53b69a47b354.png)
(1)试举例说明存在不少于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8012e76568382d926efc9cc61180fd8e.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d148722b401b72d790322700cbf101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b896f09c72d6c82c5856f441cbbd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d025f0a6755c2c4ea1c367a14d65ab2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
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2021-06-19更新
|
371次组卷
|
4卷引用: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)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)专题03 函数(1)-备战2022年高考数学(文)母题题源解密(全国乙卷)上海市奉贤中学2021届高三二模数学试题上海市奉贤中学2021届高三下学期期中数学试题
名校
6 . 对于无穷数列
,给出如下三个性质:①
;②
;③
.定义:同时满足性质①和②的数列
为“s数列”,同时满足性质①和③的数列
为“t数列”,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c7d3971d670fdcff5efa27f2cd1106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f9fe94b2594d12db5c25531d85f8b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若等比数列![]() ![]() |
您最近一年使用:0次
2021-05-11更新
|
1237次组卷
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12卷引用:考点突破14 数列-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)
(已下线)考点突破14 数列-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)(已下线)考点16 等比数列及其前n项和-备战2022年高考数学(理)一轮复习考点微专题(已下线)4.3等比数列(B 能力培优练)-2021-2022学年高二数学同步双培优检测(苏教版2019选择性必修第一册)(已下线)4.3.1-4.3.2 等比数列的概念及通项公式(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)4.3.2 等比数列的通项公式(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)(已下线)收官卷02 --备战2022年高考数学(理)一轮复习收官卷(全国甲卷) (已下线)收官卷01--备战2022年高考数学(理)一轮复习收官卷(全国甲卷)天一大联考2021届高三阶段性测试(六)理科数学试题河南省2021届高三高中毕业班阶段性测试(六)数学(理)试题河南省濮阳市2021届高三二模数学(理)试题江苏省苏州市常熟中学2021-2022学年高二上学期10月阶段学习质量检测数学试题山西省晋中市2020-2021学年高三下学期4月月考理科数学试题
名校
解题方法
7 . 已知数列
中,
,前n项和为
,且
.
(1)求
;
(2)证明数列
为等差数列,并写出其通项公式;
(3)设
,试问是否存在正整数p,q(其中
),使![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa7631bab118903861195c8c7a2665d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b297eca336cb1d9d02c17e99586cb3.png)
成等比数列?若存在,求出所有满足条件的数组(p,q);若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df945ccc3744817dc13ead49253f5fe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd76d63cc65dd133c3208868cb346440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5bbf2770cc61ba381e4a5ee5e1a26c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa7631bab118903861195c8c7a2665d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b297eca336cb1d9d02c17e99586cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cf58a39b00433d2ffbf34e86ca2f36.png)
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8 . 若无穷数列
满足:
,当
,
时.
(其中
表示
,
,…,
中的最大项),有以下结论:
①若数列
是常数列,则
;
②若数列
是公差
的等差数列,则
;
③若数列
是公比为
的等比数列,则
;
④若存在正整数
,对任意
,都有
,则
是数列
的最大项.
则其中正确的结论是_____ (写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3068733ef2ceda9f1620d5c9bcdfa542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333c77d78bdd083d1f8b7f010d05b740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37715f49f9302c190225c4fe7bbd47ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7230de53663c75658c58bbf206a0085.png)
①若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c60de05900c8d51f2cf77e5e496d93e.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8bbb4a09e0ac86bbae46222a90841.png)
③若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
④若存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2b94cbf8f1acc77ed2618d9ba5756a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
则其中正确的结论是
您最近一年使用:0次
2019-04-18更新
|
1211次组卷
|
5卷引用:专题6.5 数列的综合应用(练)【理】-《2020年高考一轮复习讲练测》
(已下线)专题6.5 数列的综合应用(练)【理】-《2020年高考一轮复习讲练测》【校级联考】江苏省泰州中学等2019届高三第二学期联合调研测试数学试题江苏省泰州中学、宜兴中学等校2019届高三4月联考数学试题(含附加题)【校级联考】江苏省高三泰州中学、宜兴中学、梁丰2019届高三第二学期联合调研测试数学试题(已下线)2019年上海市闵行区高三上学期期末质量调研数学试题
9 . 数列
是首项
,公差为
的等差数列,其前
和为
,存在非零实数
,对任意
有
恒成立,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9efeb4455e30293d412938eeea85d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.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/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0cbf1b2949a88481651780b0b4dec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2018-09-13更新
|
1597次组卷
|
5卷引用:专题3.3 数列与函数、不等式相结合问题 -玩转压轴题,进军满分之2021高考数学选择题填空题
(已下线)专题3.3 数列与函数、不等式相结合问题 -玩转压轴题,进军满分之2021高考数学选择题填空题(已下线)专题02 数列(第二篇)-备战2020高考数学黄金30题系列之压轴题(新课标版)【全国市级联考】江西省南昌市2017-2018学年度高三第二轮复习测试文科数学(五)试题【全国市级联考】江西省南昌市2017-2018学年度高三第二轮复习测试卷理科数学(五)试题2020届河北省部分重点高中高三上学期期末数学(理)试题
10 . 设数列
的各项均为正数,前
项和为
,对于任意的
成等差数列,设数列
的前
项和为
,且
,若对任意的实数
(
是自然对数的底)和任意正整数
,总有
.则
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