名校
1 . 已知集合
(
且
),
,且
.若对任意
,
,当
时,存在
,使得
,则称
是
的
元完美子集.
(1)判断下列集合是否是
的3元完美子集,并说明理由;
①
;
②
;
(2)若
是
的3元完美子集,求
的最小值;
(3)若
是
(
且
)的
元完美子集,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952f1e0ce5bd53a6d5e8bb07ea2da5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410a811a99d6f15164cdda4597323168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dd50a4fd2329323aa21597e8ff664b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e676073a8d2acb1678fdc705e33f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aadf01e5fac133cf390407bfad26b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d169a02afabbe304cf64b355bf71742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断下列集合是否是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49972f77c4c3b89116f02cbaba7f9089.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc21b9d3aa5f307d9c9d63ffaf68dc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfbdcd7014f79de428c1d5e6525aecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0604cb71df25c9b90c5d7521d3edd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8ab57234dfc54a5315381c59c94f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717995559c925685dacedc60be48fd03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf7c557b1aadac2ee7012fb1e1ba5f8.png)
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2022-05-12更新
|
733次组卷
|
4卷引用:北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题
北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题重庆市杨家坪中学2022-2023学年高一上学期10月月考数学试题(已下线)专题16 数列新定义题的解法 微点2 数列新定义题综合训练北京市第二中学2022—2023学年高一下学期第六学段阶段性考试数学试题
名校
2 . 素数又称质数,是指在大于
的自然数中,除了
和它本身以外不再有其他因数的自然数.早在
多年前,欧几里德就在《几何原本》中证明了素数是无限的.在这之后,数学家们不断地探索素数的规律与性质,并取得了显著成果.中国数学家陈景润证明了“
”,即“表达偶数为一个素数及一个不超过两个素数的乘积之和”,成为了哥德巴赫猜想研究上的里程碑,在国际数学界引起了轰动.如何筛选出素数、判断一个数是否为素数,是古老的、基本的,但至今仍受到人们重视的问题.最早的素数筛选法由古希腊的数学家提出.
年,一名印度数学家发明了一种素数筛选法,他构造了一个数表
,具体构造的方法如下:
中位于第
行第
列的数记为
,首项为
且公差为
的等差数列的第
项恰好为
,其中
;
.请同学们阅读以上材料,回答下列问题.
(1)求
;
(2)证明:
;
(3)证明:
①若
在
中,则
不是素数;
②若
不在
中,则
是素数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abb59695562b3a1295a251dc97da700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00860a6a9f7275e3d61e519b63802dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc975755665e2675c150f52821609f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
,具体构造的方法如下:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c9ee6c50000eef418c6103ecf721dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637ba0eba55f2fe7a0d03555056abdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c5fabeba3f3212955d9e282cd5482b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bbc1c45063bba6f24c99a3e30b9fd5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164ae1d08f223df4fa8df94bad8edd57.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de075cbe45f637a11f53685a018e340a.png)
(3)证明:
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbac458da41f3d58829f20be4781d50d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbac458da41f3d58829f20be4781d50d.png)
您最近一年使用:0次
2022-04-01更新
|
1678次组卷
|
4卷引用:北京市门头沟区2022届高三一模数学试题
北京市门头沟区2022届高三一模数学试题北京市第一六一中学2022届高三考前热身训练数学试题(已下线)专题4 “素材创新”类型(已下线)第六篇 数论 专题1 数论中的特殊数 微点2 数论中的特殊数综合训练
3 . 已知数列
,若存在
使得数列
是递减数列,则称数列
是“
型数列”.
(1)判断数列
,
是否为“
型数列”;
(2)若等比数列
的通项公式为
(
),
,其前
项和为
,且
是“
型数列”,求
的值和
的取值范围;
(3)已知
,数列
满足
,
(
),若存在
,使得
是“
型数列”,求
的取值范围,并求出所有满足条件的
(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b23dffd914b2a504545c5eff45fb9d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5577308eecb36a55efbd28640b957f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b050a5503deac7f3fb564a63fa957e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
(2)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796c5e37feddf76f2dcca0089f04bce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71acdb04454c77e1e25ad4f336cccfe.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/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3961db88ada7ef2eb175db12046403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b23dffd914b2a504545c5eff45fb9d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
4 . 如图,在矩形
中,
,
,
、
分别为边
、
的中点,沿
将
折起,点
折至
处(
与
不重合),若
,
分别为线段
、
的中点,则在
折起过程中,下列选项正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/9/9/3062777936781312/3066195086860288/STEM/d2315b43b23d40649b97fcc4761edba1.png?resizew=259)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df21b7b7a47318ef2bb069450c39f1cd.png)
![](https://img.xkw.com/dksih/QBM/2022/9/9/3062777936781312/3066195086860288/STEM/d2315b43b23d40649b97fcc4761edba1.png?resizew=259)
A.![]() ![]() |
B.不能同时做到![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-09-14更新
|
638次组卷
|
9卷引用:理科数学-2020年高考押题预测卷03(新课标Ⅰ卷)《2020年高考押题预测卷》
(已下线)理科数学-2020年高考押题预测卷03(新课标Ⅰ卷)《2020年高考押题预测卷》上海市洋泾中学2020-2021学年高二下学期3月月考数学试题上海市洋泾中学2021-2022学年高二上学期10月月考数学试题(已下线)第01讲 空间直线与平面(核心考点讲与练)(2)(已下线)数学(上海B卷)(已下线)10.4 平面与平面平行(第1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必修第三册)浙江省金华十校2019-2020学年高二上学期期末考试数学试题浙江省宁波市金兰教育合作组织2020-2021学年高二上学期期中联考数学试题广东省佛山市第一中学2020-2021学年高二(重点班)上学期第一次段考数学试题
5 . 已知椭圆E:
的右焦点为F,过F作互相垂直的两条直线分别与E相交于A,C和B,D四点.
(1)四边形ABCD能否成为平行四边形,请说明理由;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
(1)四边形ABCD能否成为平行四边形,请说明理由;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9de46dfa2b66a9ea3db7e9e186fcd9c.png)
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6 . 设正整数
,集合
,对于集合
中的任意元素
和
,及实数
,定义:当且仅当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701ab98a2bf1135cd989822b0738e11d.png)
时
;
;
.
若
的子集
满足:当且仅当
时,
,则称
为
的完美子集.
(1)当
时,已知集合
,
.分别判断这两个集合是否为
的完美子集,并说明理由;
(2)当
时,已知集合
.若
不是
的完美子集,求
的值;
(3)已知集合
,其中
.若
对任意
都成立,判断
是否一定为
的完美子集.若是,请说明理由;若不是,请给出反例.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645003529ce532c0fb8008542f462aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1dbd4409c152b9d4584dc4987ea1f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e41f01126901d1d41def76204ea6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701ab98a2bf1135cd989822b0738e11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f736b66000c6c6befe2171d5090bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d81180e86359c33e5cca1d7caa1cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475081154c6beb5b0c79539ae90a97d2.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26b3c852186f8f4e70e3e631a303a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2528fbb6a59ba983d1a70c81b0886484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6baf603fa729de597e4cb0c5096befec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd84e04f63b3b274ab0bd43a3602d208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86edf057f9eade338a48f31cff55a1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0eb383920bb68fa496570c3d34dff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c76d8203805842e9a756aa2b7a453a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146c0af5412c503171a5e8701158352b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92247b24065617e962c85a52086261f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79059a3366ed1b339ba1317ce8a1e7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2021-11-04更新
|
769次组卷
|
7卷引用:北京市海淀区2022届高三上学期期中练习数学试题
北京市海淀区2022届高三上学期期中练习数学试题北京市顺义区杨镇第一中学2023届高三上学期10月月考数学试题北京市汇文中学2023届高三上学期期中考试数学试题北京市东直门中学2022-02023学年高一下学期期中考试数学试题(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(人教A版2019必修第一册)北京市陈经纶中学2023-2024学年高二上学期期中考试数学试卷
名校
解题方法
7 . 若数列
的前
项和为
,且满足等式
.
(1)求数列
的通项公式;
(2)能否在数列
中找到这样的三项,它们按原来的顺序构成等差数列?说明理由;
(3)令
,记函数
的图像在
轴上截得的线段长为
,设
,求
,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/345307b291e338fbbd2bc86a39f53164.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)能否在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771991b0812e4ee2d678982c5461b86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c9752056ebb05a8e4eee608c34046b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82433897679bbf03dab49684cbfec2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5bb9e8d8cd3f0a8c7f1c3f239bd351.png)
您最近一年使用:0次
2021-10-18更新
|
1376次组卷
|
10卷引用:上海市大同中学2021-2022学年高二上学期10月月考数学试题
上海市大同中学2021-2022学年高二上学期10月月考数学试题新疆维吾尔自治区喀什第六中学2023届高三上学期9月实用性月考(一)数学(文)试题新疆维吾尔自治区喀什第六中学2023届高三上学期9月实用性月考(一)数学(理)试题(已下线)广东省2022届高三一模数学试题变式题17-22上海市松江一中2021-2022学年高二上学期期末数学试题(已下线)专题11 数列前n项和的求法 微点5 裂项相消法求和(三)(已下线)专题15 数列不等式的证明 微点3 通项放缩法证明数列不等式(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【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)上海市嘉定区第一中学2023-2024学年高二上学期期中数学试题(已下线)期末真题必刷压轴60题(22个考点专练)-【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
8 . 已知集合
,其中
.对于
,
,定义
与
之间的距离为
.
(1)记
,写出所有
使得
;
(2)记
,
、
,并且
,求
的最大值;
(3)设
,
中所有不同元素间的距离的最小值为
,记满足条件的集合
的元素个数的最大值为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d9b434ed11c614630ad6a71bf1b196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53422543e9a9311416faf749bdda67b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1a7c3713945abc4eca8485945abf32.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/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de36ac74e2640a897dedd876abcb63b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644d2ee36439bbc01fb4f35e9d24e5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf15320a185c13d59087e9391485612.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d089503d05901e02113c0ed0bd59dff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a3b20462ba83086d0711a25ed83bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b9dbb9c52862ac974003241d68fb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2b280a6a65c9bf2f20cad5d1106080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff60dcf2b1b2484b1ba940af96d336c.png)
您最近一年使用:0次
2021-05-30更新
|
1162次组卷
|
3卷引用:北京市十一学校2021届高三综合练习数学试题
9 . 设数列
满足,
,
,设
,
.
(1)设
,
,若数列的前四项
、
、
、
满足
,求
;
(2)已知
,
,
,当
,
,
时,判断数列
是否能成等差数列,请说明理由;
(3)设
,
,
,求证:对一切的
,
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334c7decfe93aeb2feefc83cfc201aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c653177884385ae15b71438aac4e704d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55ef34345210312db273ab4981c40f6.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8579e5cafc7d374d8287c160e8fb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd71c5d9676b8dc5970adfb77971c5c.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc77c479702c0ba411cb92d32877eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9df341fe7cd5fe4733fb5e47c3e750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c876fac94ce67b364063bdc736b56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0751d726398c99f8685e782cc3c447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a87d281ea5314c8e350cb55a54a14af.png)
您最近一年使用:0次
解题方法
10 . 已知等比数列
的前
项和为
,
,
.数列
的前
项和为
,且
,
.
(1)分别求数列
和
的通项公式;
(2)若
,
为数列
的前
项和,是否存在不同的正整数
,
,
(其中
,
,
成等差数列),使得
,
,
成等比数列?若存在,求出所有满足条件的
,
,
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07404ab51f404f9411f79bd4f1fde654.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/2955370028ae5a872079c12bfedc3b4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f4aaea63f5ed002251eab217a9a86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b8d543c7d503fc1073503fc1d52faa.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/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab01dd4084e2d233f3a8a1de277f1748.png)
(1)分别求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07404ab51f404f9411f79bd4f1fde654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b8d543c7d503fc1073503fc1d52faa.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bd58bdf57dcd9496d5d273ac764123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3363b34c30552a3dc76b2f66fe5288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/11bc05f41215f9894e11d1df0465751a.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/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c10d8295cb4e4fe9284f59d86442d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9d20e9994857aefb65077b666a6a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69501a69461df9471c11e93450d14164.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/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2021-01-31更新
|
553次组卷
|
5卷引用:2023版 湘教版(2019) 选修第一册 过关斩将 第1章 综合拔高练
2023版 湘教版(2019) 选修第一册 过关斩将 第1章 综合拔高练(已下线)广东省2022届高三一模数学试题变式题17-22山东省烟台市2020-2021学年高二上学期期末数学试题(已下线)专题09 《数列》中的存在性问题-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)江西省新余市2021-2022学年高二上学期期末数学(理)试题