1 . 对任意
,函数
满足
,
,数列
的前15项和为
,数列
满足
,若数列
的前
项和的极限存在,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5621a6b6ddbd6412ec54095f3ee99667.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbf139cb950fd2d25e244a2e4b2e934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb2941a43e3279928cf9aa59b13d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc2d5ea44c605de2d85d0f654cc5d79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01347a3f2ff07802ff713dd7827482d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5621a6b6ddbd6412ec54095f3ee99667.png)
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2022-11-28更新
|
994次组卷
|
2卷引用:上海市实验学校2023届高三上学期11月月考数学试题
2 . 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
|
1711次组卷
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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
3 . 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)
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名校
4 . 已知递增的等差数列{an}的首项a1=1,且a1、a2、a4成等比数列.
(1)求数列{an}的通项公式an;
(2)设数列{cn}对任意n∈N*,都有
+…+
=an+1成立,求c1+c2+…+c2014的值
(3)若bn=
(n∈N*),求证:数列{bn}中的任意一项总可以表示成其他两项之积.
(1)求数列{an}的通项公式an;
(2)设数列{cn}对任意n∈N*,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31451cd32725ea067ca65f8919748a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7df63be4f44032b7c7b2716cb5cbd3.png)
(3)若bn=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed9925a0e08120e9d2d7846cbc45bc5.png)
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5 . 如图,一质点
从原点
出发沿向量
到达点
,再沿
轴正方向从点
前进
到达点
,再沿
的方向从点
前进
达到点
,再沿
轴正方向从点
前进
达到点
,
,这样无限前进下去,则质点
达到的点的坐标是
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/aea82d26-ee01-4c63-97a5-c48565d33809.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429033fc78f59859f69857e171d7423a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366596137b12cbfe42c0e94fdf7ce6f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99198f470bfb3066e5821184426ccc30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8c162ee7c75aa5f5cbd196b18cc239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee065106d26c2b0aba3fec48c4536f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f782d70309802445202487eee751cbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/aea82d26-ee01-4c63-97a5-c48565d33809.png?resizew=180)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2019·上海浦东新·三模
6 . 已知数列
是以
为公差的等差数列,数列
是以
为公比的等比数列.
(1)若数列
的前
项和为
,且
,
,求整数
的值;
(2)若
,
,
,试问数列
中是否存在一项
,使得
恰好可以表示为该数列中连续
项的和?请说明理由;
(3)若
,
,
(其中
,且
是
的约数),求证:数列
中每一项都是数列
中的项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/7e1e25a2ced335ad333c82e9871e8e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0c311a01b1848ca5b8e07b78ccb0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae323cdb00fe1c948dfa22f71eb3b885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ee3c5217835dabd18b10110b88c01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699e55c211a6e091cc7a9d2cde3ed981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1ed1737f979a5c1b46fce63d84e85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111684df67e3120e325ddf5ba6034455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8846d1da2a612268f8cbd88d017d7dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ff93072dc3e904ca0bb0064577d35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704f630e5bbdd1537a0995918efb0b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b90a5824920ac2f5a7102a0e2d827c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
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