名校
1 . (1)已知m是实数,集合
,
.求证:“
”是“
”的充要条件.
(2)设
.证明:若
是奇数,则n也是奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0274ba49bbad8b3179d628e3d7025cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6e153c5b9e2e807125326fd904644c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e851796d98eb47a8d17f4e1b4cea196.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f02d5c8eec434a3f90348d770a2e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
您最近一年使用:0次
2020-10-27更新
|
454次组卷
|
8卷引用:上海奉贤区致远高级中学2020-2021学年高一上学期10月月考数学试题
上海奉贤区致远高级中学2020-2021学年高一上学期10月月考数学试题上海市奉贤区致远高级中学2021-2022学年高一上学期10月评估数学试题上海市奉贤区致远高级中学2022-2023学年高一上学期10月月考数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高一上学期9月月考数学试题(已下线)1.2 充分条件与必要条件(第2课时)(已下线)专题04常用逻辑用语-【倍速学习法】(沪教版2020必修第一册)(已下线)1.4 充分条件与必要条件(5大题型)精练-【题型分类归纳】(已下线)专题04充分条件与必要条件-【倍速学习法】(人教A版2019必修第一册)
名校
解题方法
2 . 已知函数
.
(1)若
满足
为R上奇函数且
为R上偶函数,求
的值;
(2)若函数
满足
对
恒成立,函数
,求证:函数
是周期函数,并写出
的一个正周期;
(3)对于函数
,
,若
对
恒成立,则称函数
是“广义周期函数”,
是其一个广义周期,若二次函数
的广义周期为
(
不恒成立),试利用广义周期函数定义证明:对任意的
,
,
成立的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17422461d5ec2bff93452619c6b774f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b727eb9da56be079445321cf61cf26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be344d1925b25e44f3f8b34d2c193ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b186e49220460b09f85519aa657527b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf03e1296f7f5bb315c87893caee079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4056806dc4a2f28e267f879b6f5c0079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c204be088a8fc6c096eedd5b1e7dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(3)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06d64b48da95b74aa5e12bc5da127dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c90d0f5f17344c0eb75c2aea394bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183ba00d69af06d9a950469b38cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a35277c37144276ead40bb74a51481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183ba00d69af06d9a950469b38cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb05fd7662d05b9e2051b044de722840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05dd02b6f561dcf94bab8a3160108d5.png)
您最近一年使用:0次
2020-08-25更新
|
1049次组卷
|
6卷引用:上海市建平中学2019届高三下学期5月月考数学试题
上海市建平中学2019届高三下学期5月月考数学试题2019年上海市建平中学高三三模数学试题(已下线)专题2.3 函数的奇偶性与周期性(精讲)-2021年高考数学(理)一轮复习学与练(已下线)专题2.3 函数的奇偶性与周期性(精讲)-2021届高考数学(理)一轮复习讲练测(已下线)3.2函数的基本性质-2020-2021学年高一数学同步课堂帮帮帮(人教A版2019必修第一册)(已下线)专题03 函数的概念与性质(模拟练)-2
名校
3 . 平面直角坐标系
中,已知
是直线
上的
个点(
,
均为非零常数).
(1)若数列
成等差数列,求证:数列
也成等差数列;
(2)若点
是直线
上的一点,且
,求
的值;
(3)若点
满足
,我们称
是向量
的线性组合,
是该线性组合的系数数列.证明:
是向量
的线性组合,则系数数列的和
是点
在直线
上的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd0dc3af8a4540cbecb42bfd1a40c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb91abeed60da0f999b46e337957dec9.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6bed084dfe8eb8fedc2b8e6263abc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6f19b84484b5480ea2100165abfd81.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d583c7ee5938cf498bbf227a3d759bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee557308fa0f1384b6e724dfed5aeb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a2bfe2fbda2c89f1e351d351f65186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee557308fa0f1384b6e724dfed5aeb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a2bfe2fbda2c89f1e351d351f65186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9d32a80797d4ba989dc291d6e154d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
4 . 已知二次函数
.
(1)若等式
恒成立,其中
,
,
为常数,求
的值;
(2)证明:
是方程
有两个异号实根的充要条件;
(3)若对任意
,不等式
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
(1)若等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e712bf30e058bf1d343f46a7b5205db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432793c48a89aa2568c884f0283c5a9a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4944b18a1daae0480089124e5551107f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e72f73a14e6449fe4a18bd0fa9b739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623df532d1c7a31036b5d6e2aee98756.png)
您最近一年使用:0次
2023-10-09更新
|
753次组卷
|
4卷引用:上海市莘庄中学2023-2024学年高一上学期10月月考数学试题
上海市莘庄中学2023-2024学年高一上学期10月月考数学试题四川省仁寿第一中学校南校区2023-2024学年高一上学期第二次质量检测(10月)数学试题上海师范大学附属中学闵行分校2023-2024学年高一上学期期中数学试题(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列
名校
5 . 设
为
的三边,求证:方程
与
有公共根的充要条件是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ec18aa8ab6f4a4e70722e4df77c9c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4417c3fb5eed62eabd95f8c54782276d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa61c1a7fdfa101523bf8b6eaaff65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc1ba2766874730daaad7d3bb7a8ee4.png)
您最近一年使用:0次
2022-08-13更新
|
922次组卷
|
29卷引用:上海市华东师范大学第二附属中学2016-2017年高一上学期第一次月考数学试题
(已下线)上海市华东师范大学第二附属中学2016-2017年高一上学期第一次月考数学试题黑龙江省宾县一中2019-2020学年高二上学期第一次月考数学(文)试卷黑龙江省哈尔滨市宾县一中2019-2020学年高二上学期第一次月考数学(理)试题广东省惠州市第一中学2021-2022学年高一上学期第一次月考数学试题江苏省盐城市射阳中学2022-2023学年高一上学期第一次月考数学试题湖北省新高考联考协作体2022-2023学年高一上学期10月月考数学试题广东省汕头市潮阳一中明光学校2023-2024学年高一上学期第一次检测(10月)数学试题人教B版(2019) 必修第一册 必杀技 第一章素养检测(已下线)专题02 集合与常用逻辑用语(同步练习)-2021年高考一轮数学(文)单元复习一遍过(已下线)专题02 集合与常用逻辑用语(同步练习)-2021年高考一轮数学(理)单元复习一遍过(已下线)专题02 集合与常用逻辑用语(同步练习)-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题1.4 充分条件与必要条件-2020-2021学年高一数学尖子生同步培优题典(人教A版2019必修第一册)(已下线)1.4 充分、必要条件(精炼)-2020-2021学年一隅三反系列之高一数学新教材必修第一册(人教版A版)(已下线)第1章 集合与常用逻辑用语-2021-2022学年高一数学课后培优练(人教A版2019必修第一册)(已下线)专题2.1 充分条件、必要条件、充要条件-重难点题型精讲-2021-2022学年高一数学举一反三系列(苏教版2019必修第一册)(已下线)专题1.7 充分条件与必要条件-重难点题型精讲-2021-2022学年高一数学举一反三系列(人教A版2019必修第一册)(已下线)专练8 集合与常用逻辑用语检测卷(A卷)-2021-2022学年高一数学上册同步课后专练(人版A版必修第一册)河南省林州市第一中学2021-2022学年高一上学期开学检测(普通班)数学试题(已下线)专题1.7 必要条件与充分条件-重难点题型精讲-2021-2022学年高一数学举一反三系列(北师大版2019必修第一册)(已下线)专题1.9 充分条件、必要条件-重难点题型精讲-2021-2022学年高一数学举一反三系列(人教B版2019必修第一册)第2章 常用逻辑用语(章末测试提高卷)-2021-2022学年高一数学同步单元测试定心卷(苏教版2019必修第一册)(已下线)专题13 充分条件与必要条件-2022年暑假初三升高一数学衔接知识自学讲义(人教A版2019)北京市昌平区新学道临川学校2021-2022学年高二下学期期中考试数学(文)试题2023版 湘教版(2019) 必修第一册 过关斩将 第1章 集合与逻辑江苏省南通市如皋中学2022-2023学年高一上学期8月综合测试数学试题(已下线)期中考试押题卷(测试范围:第1~4章)-2022-2023学年高一数学新教材同步配套教学讲义(苏教版2019必修第一册)(已下线)第06讲 充分条件、必要条件、充要条件-【暑假自学课】(苏教版2019必修第一册)(已下线)1.4 充分必要条件(精练)-《一隅三反》(已下线)专题02 常用逻辑用语压轴题-【常考压轴题】
解题方法
6 . 在数列
中,若存在常数
,使得任意
都有
,则称
是
数列.
(1)若数列
是
数列,且
,
,写出所有满足条件的数列
的前4项;
(2)已知数列
是等比数列,求证:
是
数列的充要条件是其公比为
;
(3)若
数列
满足
,
,
,设数列
的前
项和为
,是否存在正整数
、
,使得不等式
对一切
都成立?若存在,求出
、
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92346d262f286d8cffa834ab87d979c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb6e1c4c91b53f5cc97dfdf0dc00ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627e48c5ab76f5d1874c57a40d32d89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0262791cc14598c6fc5ed0937d0124.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e42e1961482c32d10aa1b3ba12a6d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a015489a920fc0f9c61f359726e7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0701f2ee93d4150457be4efaf94ce493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c83451624b13a97e0abf0f4a9b46f0.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/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac22873184ffab4a715d43c72491d816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92346d262f286d8cffa834ab87d979c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
您最近一年使用:0次
名校
7 . 设
,求证:“
是偶数”是“
是奇数”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f02d5c8eec434a3f90348d770a2e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00470075ebfa218745e54f7521ba839.png)
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名校
8 . 已知
,
为两非零有理数列(即对任意的
,
,
均为有理数),
为一无理数列(即对任意的
,
为无理数).
(1)已知
,并且
对任意的
恒成立,试求
的通项公式.
(2)若
为有理数列,试证明:对任意的
,
恒成立的充要条件为
.
(3)已知
,
,对任意的
,
恒成立,试计算
.
![](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/ed6af1644737a2948f30308a168ff07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6af1644737a2948f30308a168ff07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50a4b1e4f8b1d044300df7ef8205c31.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2391202d5ea5ed1802af734a78583961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d36e322a05765061155210df4176aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c404f6958b9613226e380b16dba8f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244d2564c2bff56c566e7990f570d549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dfd310df0a4f42cf64dc1bed85f816.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fe6fdf0d6443ef6e5f34d9741a0759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25260e98fe082f4ec2b6273aa17e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbc42581b47d7665015dc5c22922bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
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2020-09-06更新
|
646次组卷
|
10卷引用:上海市实验学校2017届高三上学期第四次月考数学试题
上海市实验学校2017届高三上学期第四次月考数学试题上海市建平中学2019届高三下学期5月月考数学试题2016届上海市七宝中学高三模拟理科数学试卷2016届上海市七宝中学高三模拟考试数学(理)试卷2019年上海市建平中学高三三模数学试题2016届上海市闵行区七宝中学高三下学期适应性考试(三模)(理)数学试题(已下线)重难点04 三角函数与解三角形-2021年高考数学【热点·重点·难点】专练(上海专用)上海市浦东新区2021届高三三模数学试题上海市大同中学2021届高三三模数学试题(已下线)考向10 三角恒等变换-备战2022年高考数学一轮复习考点微专题(上海专用)
9 . 对于给定的正整数
,若数列
满足
对任意正整数
恒成立,则称数列
是
数列,若正数项数列
,满足:
对任意正整数
恒成立,则称
是
数列;
(1)已知正数项数列
是
数列,且前五项分别为
、
、
、
、
,求
的值;
(2)若
为常数,且
是
数列,求
的最小值;
(3)对于下列两种情形,只要选作一种,满分分别是 ①
分,②
分,若选择了多于一种情形,则按照序号较小的解答记分.
① 证明:数列
是等差数列的充要条件为“
既是
数列,又是
数列”;
②证明:正数项数列
是等比数列的充要条件为“数列
既是
数列,又是
数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0981b9ded724ecec5735ced14d684bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3205ae03910cf77c8cf5b1ac7372d839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e94a2fd143f31e7981007589aed7ff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06da966dc473fe3addf33e4d25f530e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3205ae03910cf77c8cf5b1ac7372d839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db6addea8060eea6953e2faa6c3d5e9.png)
(1)已知正数项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8065f6ed7bf3568ec9df743e70a285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f14adcde2c42c774c827fb3ecef852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b287cf4370beceda3d58fb85f5f7b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(3)对于下列两种情形,只要选作一种,满分分别是 ①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
① 证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b287cf4370beceda3d58fb85f5f7b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a945987b037c1d04cbb2c875ab5569.png)
②证明:正数项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d766cbb87f501f8a0447af6104400590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6c507b32cdaeb48f3e863b4250a9d6.png)
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