1 . 从数列
中取出部分项组成的数列称为数列
的“子数列”.
(1)若等差数列
的公差
,其子数列
恰为等比数列,其中
,
,
,求
;
(2)若
,
,判断数列
是否为
的“子数列”,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec07a126ada2c921c5b4337f77854cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaa992a449b828df0ff545e233b279b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84f592310f4b9637b225cab622b2aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d438131add92b51c4e0b06ec6aff581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373ecb5531c1593f13a0ed081597b3cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d38a1171131b1a1f3f70ca2117be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221016d4bfafd5693a4e767fcf6a2559.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
2019-11-14更新
|
370次组卷
|
3卷引用:上海市七宝中学2018-2019学年高二下学期3月月考数学试题
上海市七宝中学2018-2019学年高二下学期3月月考数学试题上海市闵行区七宝中学2018-2019学年高二下学期开学考试数学试题(已下线)4.2 等比数列的前n项和(第2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(沪教版2020选择性必修第一册)
2 . 已知非零向量列
满足:
,
,(
,
).
(1)证明:数列
是等比数列;
(2)向量
与
的夹角;
(3)设
,将
中所有与
共线的向量按原来的顺序排成一列,记作
,令
,
为坐标原点,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a85cead056c360dc3a253f4b33e80e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9a808551e595b00f9ee59107a3a3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ea9931443752f200ec29a47462e7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4684c93e9c029f9b3b13b17b27fbe616.png)
(2)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2121e9cac7d80abd7c6a0c0de5c67a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1522e062601bd8cbf0e1dfb46dc99479.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa9e0012bc248a4e53d85a5e74720c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51ed353422670f241fa8bbd5e40cef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d970a4c8abf3fe4da3382206086a6cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b338f70f70c227f0d32028f0cdb582e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc17566d149fbc091fc4c0b06074c046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
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3 . 函数
满足
,当x,
时,
恒成立,又
满足:
,
,设
.
(1)证明:数列
是等比数列,并求
的表达式:
(2)是否存在正整数m,使得对任意
,都有
成立,若存在,求出m的最小值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f0c3fa7e80287ff21fcdb1b3c9b41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1947266214c98cfdeea15425a47de17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773932788bfccf3f2a43207a159c33c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b014f066b238e9bc9fd0806791dcfd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02755813a357cd06484b6fb570dee8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df49f07a4e2a6dfe4dca3763364f762c.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f37c589447bba4e81b0fa9b7cd15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc3e6b5177f21e68eea45da9e0bf6e1.png)
(2)是否存在正整数m,使得对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aba95f1aacf777532636f8409030f69.png)
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4 . 若
是递增数列,数列
满足:对任意
,存在
,使得
,则称
是
的“分隔数列”.
(1)设
,证明:数列
是
的分隔数列;
(2)设
是
的前n项和,
,判断数列
是否是数列
的分隔数列,并说明理由;
(3)设
是
的前n项和,若数列
是
的分隔数列,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0e1bf4089f2bca396ea88ace87280b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4c7656230ac2f2448794c2dfeddf50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a088f7a49c2cc904eb8a2ef63648f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e860496fcd95208b86d5383f43ec4858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4b847f08d34be2f197378f57641f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b5d1c18737c9607a94a3990ee40ec5.png)
您最近一年使用:0次
2019-08-17更新
|
266次组卷
|
2卷引用:上海市莘庄中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
5 . 给定整数
(
),设集合
,记集合
.
(1)若
,求集合
;
(2)若
构成以
为首项,
(
)为公差的等差数列,求证:集合
中的元素个数为
;
(3)若
构成以
为首项,
为公比的等比数列,求集合
中元素的个数及所有元素之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54d41b965c7b1771c84fabb87ae6258.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f77cadcea108fc0b1f680a8840a274c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2019-02-01更新
|
577次组卷
|
6卷引用:上海市七宝中学2020届高三上学期11月月考数学试题
上海市七宝中学2020届高三上学期11月月考数学试题上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题上海市曹杨二中2019-2020学年高二上学期期末数学试题北京市密云区第二中学2024届高三上学期10月月考数学试题北京市东城区景山学校2021届高三上学期期中数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f168350df63ffad561fe335f8d4b805.png)
常数
)满足
.
(1)求出
的值,并就常数
的不同取值讨论函数
奇偶性;
(2)若
在区间
上单调递减,求
的最小值;
(3)在(2)的条件下,当
取最小值时,证明:
恰有一个零点
且存在递增的正整数数列
,使得
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f168350df63ffad561fe335f8d4b805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057db09504e1a3e62cd7fc678a7c31ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de99d710db8879ae5e252dd7a80dbba.png)
(1)求出
![](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/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b4fc6f2418a01a22e093134b432574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ebbcccecea9155858e048ba3828602.png)
您最近一年使用:0次
2016-12-03更新
|
1128次组卷
|
4卷引用:2014届上海市虹口区高三5月模拟考试理科数学试卷
(已下线)2014届上海市虹口区高三5月模拟考试理科数学试卷上海市建平中学2015届高三下学期4月月考数学试题上海市普陀区长征中学2018-2019学年高三上学期期中数学试题上海市闵行区七宝中学2016-2017学年高三上学期期中数学试题
13-14高三·北京西城·期末
名校
7 . 在数列
中,
.从数列
中选出
项并按原顺序组成的新数列记为
,并称
为数列
的
项子列.例如数列
、
、
、
为
的一个
项子列.
(1)试写出数列
的一个
项子列,并使其为等差数列;
(2)如果
为数列
的一个
项子列,且
为等差数列,证明:
的公差
满足
;
(3)如果
为数列
的一个
项子列,且
为等比数列,证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8385314c25d6198c23842d1eec7fdc9c.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a07315a54049e967b8484b1aacb121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1c4a517e42197bc0d20fdbbe261758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)试写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e382e9db36ee214e23d73858dc4c9ed.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb7a1a4dbb8ee2bb25401e333984867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8385314c25d6198c23842d1eec7fdc9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4fde290f6f17f43ba4ea1efefe9660.png)
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