名校
1 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.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/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2023-07-17更新
|
543次组卷
|
5卷引用:重庆市南开中学校2023-2024学年高一上学期开学考试数学试题
重庆市南开中学校2023-2024学年高一上学期开学考试数学试题北京市顺义区2022-2023学年高一下学期期末质量监测数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
2 . 记无穷数列
的前n项中最大值为
,最小值为
,令
.
(1)若
,请写出
的值;
(2)求证:“数列
是递增的等差数列”是“数列
是递增的等差数列”的充要条件;
(3)若
,求证:存在
,使得
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293570f1284f5161d0c9e83c1aef7777.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d207b73fd6b888db038e3e0d17383958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447e5baee4f7518706498d4aca7553b.png)
(2)求证:“数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95a1e259bc8ae8f932a8743d63fc37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49684a3fb6e58fe4471f000528353656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac212ee4717d64901197c1a0a734f60.png)
您最近一年使用:0次
2023-03-26更新
|
483次组卷
|
2卷引用:北京市第八十中学2024届高三下学期开学考试数学试卷
名校
3 . 设
,
,则
三个数( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f57f35fbbb5d288691dda630a44961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ae1b6afc99d38f6f4423dd82fdc687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.都小于4 | B.至少有一个不大于4 |
C.都大于4 | D.至少有一个不小于4 |
您最近一年使用:0次
2019-10-30更新
|
2838次组卷
|
10卷引用:江西省赣州市赣县第三中学2020-2021学年高二2月入学考试数学(理)试题
江西省赣州市赣县第三中学2020-2021学年高二2月入学考试数学(理)试题安徽省六安市第一中学2019-2020学年高二上学期第一次段考数学(文)试题江西省新余市第一中学2019-2020学年高二下学期第一次段考数学(理)试题(已下线)3.4+基本不等式(1)-2020-2021学年高二数学课时同步练(人教A版必修5)(已下线)专题04+常用逻辑用语(2)(反证法)-2020-2021学年新教材高一数学秋季辅导讲义(沪教版2020)(已下线)3.2 基本不等式(2)应用与难点(课堂培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)3.2 基本不等式安徽省合肥市第八中学2020-2021学年高二下学期期中理科数学试题(已下线)专题04 基本不等式压轴题-【常考压轴题】(已下线)专题02 一元二次函数、方程和不等式3-2024年高一数学寒假作业单元合订本
4 . 有限数列
:
,
,…,
.(
)同时满足下列两个条件:
①对于任意的
,
(
),
;
②对于任意的
,
,
(
),
,
,
,三个数中至少有一个数是数列
中的项.
(1)若
,且
,
,
,
,求
的值;
(2)证明:
,
,
不可能是数列
中的项;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
①对于任意的
![](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/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
②对于任意的
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247bf9c5c1ad2b3e50952ec92afa3ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f52783e7a39f438adf08ef7d05d8c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8343838b2f9943d83231763b2078136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be0f858adaefa50f7c99e6062fdf2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ad229a63bc75abfa8f5a48fe99038f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3859890e300f470dcf4a215249da07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-11-19更新
|
1228次组卷
|
10卷引用:北京市汇文中学教育集团2023-2024学年高三下学期开学考数学试题
北京市汇文中学教育集团2023-2024学年高三下学期开学考数学试题2015届北京市海淀区高三下学期期中练习(一模)理科数学试卷北京市北京师范大学第二附属中学2019-2020学年高二上学期期中数学试卷北京市第五十七中学2019-2020学年高二上学期期中考试数学试题重庆市缙云教育联盟2022届高三上学期第O次诊断性检测数学试题(已下线)北京市第四中学2022届高三下学期(三模)保温练习数学试题北京卷专题18数列(解答题)(已下线)北京市第四中学2023届高三数学保温测试试题北京市十一学校2022届高三下学期2月诊断数学试题北京市第八中学2024届高三上学期10月练习数学试题
名校
解题方法
5 . 对于数集X={-1,x1,x2,
,xn},其中
,n ≥ 2,定义向量集
,若对任意
,存在
,使得
,则称X具有性质P.例如{-1,1,2}具有性质P.
(1)若x > 2,且{-1,1,2,x}具有性质P,求x的值;
(2〉若X具有性质P,求证:1 ∈X ,且当xn >1 时,x1= 1;
(3)若X具有性质P,且x1= 1 ,x2 =q (q为常数),求有穷数列x1,x2,
,xn的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0040b12a13d03d5f1c6c1f80ac0365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac4d197ead9c1bc27b05aedac23ad79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122d308af408739c2717376e932122d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c6bb4424eb1e5ab02b8ac83fd6ad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8de3dabcc3150fd539ac97718ba10c5.png)
(1)若x > 2,且{-1,1,2,x}具有性质P,求x的值;
(2〉若X具有性质P,求证:1 ∈X ,且当xn >1 时,x1= 1;
(3)若X具有性质P,且x1= 1 ,x2 =q (q为常数),求有穷数列x1,x2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
您最近一年使用:0次
2021-08-29更新
|
538次组卷
|
6卷引用:北京市北京八中2018届高三第二次月考数学理科试题
20-21高三上·上海浦东新·阶段练习
名校
解题方法
6 . 已知
、
与
、
是4个不同的实数,若关于
的方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15dce0a16618c3244c4e4799be1ec7a.png)
的解集
不是无限集,则集合
中元素的个数构成的集合为___________ .
![](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/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15dce0a16618c3244c4e4799be1ec7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76cf6f76dbdd4f6d740e7b72d80118ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2020-12-13更新
|
554次组卷
|
3卷引用:上海市位育中学2021届高三下学期开学考试数学试题
名校
解题方法
7 . 已知数列
是由正整数组成的无穷数列,若存在常数
,使得
,对任意的
成立,则称数列
具有性质
.
(1)分别判断下列数列
是否具有性质
;(直接写出结论)①
;②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
(2)若数列
满足
,求证:“数列
具有性质
”是“数列
为常数列的充分必要条件;
(3)已知数列
中
,且
.若数列
具有性质
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fce92044e29a9492af22510e55950e8.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/c5353a6e81f046535210ca84b06c6f3c.png)
(1)分别判断下列数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baaa78864aa6e47a10b0f1409e7c2b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15ffa7fecea3704dc892ea8cd513c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340e10c8ee75b0d186f6dd2551aa1689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baaa78864aa6e47a10b0f1409e7c2b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)已知数列
![](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/7c031ea3d46e3f04e575f817341bad06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8bd5e21c1d6a4d3ce264b691eb578b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2021-08-26更新
|
403次组卷
|
4卷引用:高二数学开学摸底考02(上海专用)(测试范围:必修三+选修一)-2023-2024学年高二数学下学期开学摸底考试卷
(已下线)高二数学开学摸底考02(上海专用)(测试范围:必修三+选修一)-2023-2024学年高二数学下学期开学摸底考试卷2020届北京市海淀区高三一模数学试题北京市第一七一中学2020-2021学年高二下学期期中考试数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大题型)(练习)
12-13高三上·江苏无锡·期中
名校
8 . 已知数列
的前
项和
满足
,数列
满足
.
Ⅰ
求数列
和数列
的通项公式;
Ⅱ
令
,若
对于一切的正整数
恒成立,求实数
的取值范围;
Ⅲ
数列
中是否存在
,且
使
,
,
成等差数列?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08f2e9372fdc1f3f392ac22fd4d7b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5e3f1191fa8c6f609335be79b811bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbcc4d79a9b2b023dd9c3ee5ec06b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d4713864382d5f93012d84be9b3d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c512b2cc5ff43e0cdefe46c8caeeb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25729a814bd28938e92a8d029d1f27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152cc288bddfa3fb9e029f45db738073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee09e0b22fe975a2922f2dc636e09b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfb9e5ccc5b8f9cb10c4595a9fa2878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875a08b714fe25238bf663de3e190f77.png)
您最近一年使用:0次
2018-12-12更新
|
947次组卷
|
4卷引用:2020届北京市海淀区首都师范大学附属中学高三开学考试数学试题
2020届北京市海淀区首都师范大学附属中学高三开学考试数学试题北京市海淀区中关村中学2022届高三上学期开学测试数学试题(已下线)2012届江苏省无锡市高三上学期期中考试数学【区级联考】北京市通州区2019届高三上学期期中考试数学(理)试题
9 . 数列
的各项均为整数,满足:
,且
,其中
.
(1)若
,写出所有满足条件的数列
;
(2)求
的值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c443dd1ce0f02cae28a35d69816031a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae17052168f340cb0757dc1ec0959489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65560724cdbf1a53160359333bba73b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9efeb4455e30293d412938eeea85d5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2309691b0e1b023bcb8d485cce6f1721.png)
您最近一年使用:0次
2020-03-12更新
|
421次组卷
|
2卷引用:北京市海淀区北京交大附中2024届高三下学期3月开学诊断练习数学试题
10 . 将
阶数阵
记作
(其中,当且仅当
时,
).如果对于任意的
,当
时,都有
,那么称数阵
具有性质
.
(Ⅰ)写出一个具有性质
的数阵
,满足以下三个条件:①
,②数列
是公差为2的等差数列,③数列
是公比为
的等比数列;
(Ⅱ)将一个具有性质A的数阵
的每一列原有的各数按照从上到下递增的顺序排列,形成一个新的
阶数阵,记作数阵
.试判断数阵
是否具有性质A,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f54b17a7fbf7220c441081faa1b89bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4561d9f0192fefa4fbe13b873870b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e531b92668d0247db929cc5eb43d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8869723ad5015e5124d0f5def782c23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e04de3b82616c97e5292ee36668d7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166db5a2fdd71595bd7e5aedf185dcf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae327610a1b9d6e2f40e086024d4753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4561d9f0192fefa4fbe13b873870b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅰ)写出一个具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d3c740f55aaa7517911b64c10a3df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35aea718ef448f4dd96ff22dca1f9628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f97e878e36da1ad81ae8f90dab5995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dec760cb610a155a4ad7cf6edd01a14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(Ⅱ)将一个具有性质A的数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4561d9f0192fefa4fbe13b873870b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac426c29f630e98c45ecc9a33e2d04b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac426c29f630e98c45ecc9a33e2d04b.png)
您最近一年使用:0次
2019-01-17更新
|
475次组卷
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2卷引用:北京市八一学校2024届高三上学期开学摸底考试数学试题