名校
1 . 已知各项均不为零的数列
的前
项和为
,
,
,
,且
,则
的最大值等于_________ .
![](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/bbe7bdaaf8b0adf10bf2ef6c1255b1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fdd606e80f1f7c0a559d259d381c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1b4a3abe5719814ca6497520b1ba8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5b083c3cf55f65f882796e960f4c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f422edb72f7e1d5529a5570feb77df.png)
您最近一年使用:0次
2023-02-06更新
|
705次组卷
|
4卷引用:福建省宁德第一中学2020-2021学年高二上学期开学检测数学试题
福建省宁德第一中学2020-2021学年高二上学期开学检测数学试题上海市行知中学2020-2021学年高二下学期期中数学试题(已下线)高二下期中真题精选(压轴40题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
名校
解题方法
2 . 对于数列
,若存在常数
,对任意的
,恒有
,则称数列
为
数列.
(1)首项为1,公比为
的等比数列
是否为
数列?请说明理由;
(2)设
是数列
的前
项和,若数列
是
数列,那么数列
是否为
数列?若是,请说明理由;若不是,请举出一个例子;
(3)若数列
,
都是
数列,求证:数列
是
数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d4f5886b62640f2638d7e9580a51d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866d003eaa6187770f751425fac96dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d4f5886b62640f2638d7e9580a51d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
(1)首项为1,公比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc0bdefe6ea4cc508dd42ee6061106b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
您最近一年使用:0次
2023-01-31更新
|
426次组卷
|
2卷引用:北京一零一中学2021届高三上学期10月统考(二)数学试题
真题
解题方法
3 . A是由定义在
上且满足如下条件的函数
组成的集合:①对任意的
,都有
;②存在常数
,使得对任意的
,都有
.
(1)设
,证明:
;
(2)设
,如果存在
,使得
,那么这样的
是唯一的;
(3)设
,任取
,令
,证明:给定正整数k,对任意的正整数p,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de71d25c72850e383a4c841eed0db99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2775ffdf695af2d263f0ea93ac5904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4031c9cbbcbbecfc0a8ca5490647e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5d880d349c00a3f81f830bb35e1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d03b29af4e3206af656a142d17657f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799650ddf5fb8e7c91cf59163aa1b7a4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1dbdb8423d86a92629b081ae2b2154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5528f643fe7e0449e48c8f81b16b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e599070e5874ed4a9478f5260b98e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0d7024ce3371628f09963f9a976ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dcca902b1982e13aeea5d094bb6016.png)
您最近一年使用:0次
4 . 设
,如图,已知直线
及曲线
,C上的点
的横坐标为
.从C上的点
作直线平行于x轴,交直线l于点
,再从点
作直线平行于y轴,交曲线C于点
.
的横坐标构成数列
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/92c5f778-0f93-434c-907c-a08340ef4426.png?resizew=190)
(1)试求
与
的关系,并求
的通项公式;
(2)当
时,证明
;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2df29bc4b98cfcc6a3237b5fef779e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c190e3498ab082d575c24a1a66b6da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324872ecd041f6174655abf830019615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a753812145824f98f997029f5a7439e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908164d96d0438801a4f4aefebdf3aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e240e2923edaf859466663a10ebe77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/92c5f778-0f93-434c-907c-a08340ef4426.png?resizew=190)
(1)试求
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57755d3087d086f83e1b6f37723d2869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4ee8097d2c1659752dda9d86603f70.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa634182cc0ec75b9fd5d0db429d74b9.png)
您最近一年使用:0次
名校
解题方法
5 . 已知数列
满足
,
,
,
是数列
的前
项和,则下列结论中正确的是( )
![](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/194463e3b011603ff59c0789bcb65c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.![]() | B.![]() |
C.![]() | D.存在常数![]() ![]() |
您最近一年使用:0次
6 . 已知函数
各项均不相等的数列
满足
.令
.给出下列三个命题:(1)存在不少于3项的数列
使得
;(2)若数列
的通项公式为
,则
对
恒成立;(3)若数列
是等差数列,则
对
恒成立,其中真命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e115dd0cb0c28b33cdc1a43e9be779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6044fe76e20b5da7861f3d9b3f3143e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec26010780db181e89a51f780743f6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d87a9b5258b1a5eaee3b71004a4838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8fcccbb1234ad67314c96f9856e240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1a21f360eab1fb27b8cc15db4c04a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6273df1952961f128bb340bc28e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2cc49cadf5bf94f8df8318fa7bd519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
A.(1)(2) | B.(1)(3) | C.(2)(3) | D.(1)(2)(3) |
您最近一年使用:0次
2020-11-15更新
|
1712次组卷
|
6卷引用:2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题
2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题(已下线)数学-6月大数据精选模拟卷04(上海卷)(满分冲刺篇)上海市南洋模范中学2021届高三上学期期中数学试题(已下线)考向03 函数及其性质-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15 等比数列-备战2022年高考数学一轮复习考点微专题(上海专用)上海交通大学附属中学2021-2022学年高一下学期5月线上月考数学试题
解题方法
7 . 已知数列
的前n项和为
,满足
.
(1)求证:
是等差数列;
(2)已知
是公比为q的等比数列,
,
,记
为数列
的前n项和.
①若
(
是大于2的正整数),求证:
;
②若
(i是某个正整数),求证:q是整数,且数列
中的每一项都是数列
中的项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25673902449184f5727cbc786aa82a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd56c886d76991ec450d4aa1b7a6174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5274adf9ab52f082fb4f8f557e701621.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25673902449184f5727cbc786aa82a0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf92b5d061e45e1c720cdf93409ae75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd95636852e2bc9a178e2e9c012175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faab43e42c933f4a72763ff298844db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee956329e95a172d86c86b2f6af7aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd4f7a23f369403dea2892fee983c69.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac52d20d7bb3a6631f5035ef18b64c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
8 . 设
是无穷正项等比数列,公比为
.对于正整数集
的子集
,若
,定义
;若
,定义
.
(1)若
,
,
,求
;
(2)设
.若
、
是
的非空有限子集且
,求证:
;
(3)若对
的任意非空有限子集
、
,只要
,就有
,求公比
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2107216f6f7f012fd631c5da84365b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbbcfe1c221cbfee862634526d6c1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e745fd938663191ae254f18b979afc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c17e4e98aa1080cf1752257a113af45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f45f5bc7c648c0e8924b4fa7b1ad08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799a57bb07e4d32501018027843b7d53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf414809032abdd0d6b259228275757.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4099a6a331e90aa8b7fdd3c113673896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65b558a0445c59c83fa28d9ca0f37.png)
(3)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3675d10cb915e25bf349649b2e20e08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfaafb17097504a9bdd0317a0ecabe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
您最近一年使用:0次
名校
解题方法
9 . 设数列
满足
,其中c为实数,数列
的前n项和是
,下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d49a6688994daabc49924716e6ad847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea49f8a2b98b542b1ebb2ac813346c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.c∈[0,1]是![]() | B.当c>1时,![]() |
C.当c<0时,不存在c使![]() | D.当![]() ![]() |
您最近一年使用:0次
2020-08-12更新
|
1507次组卷
|
2卷引用:浙江省2020届高三新高考模拟试题心态卷数学试题
10 . 已知在每一项均不为0的数列
中,
,且
(
、
为常数,
),记数列
的前
项和为
.
(1)当
时,求
;
(2)当
、
时,
①求证:数列
为等比数列;
②是否存在正整数
,使得不等式
对任意
恒成立?若存在,求出
的最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639a6bb038215e3615f53ce2faf9f93f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
①求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ccf5dbc6bf9cab46c3c9a6a11c84fcd.png)
②是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ecce6bf54d9afecb470ce2469397cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-07-28更新
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1164次组卷
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4卷引用:江苏省苏州市昆山市2020届高三下学期6月高考模拟数学试题