名校
解题方法
1 . 已知向量
满足
,
,则
的最大值等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a28ff4f6d654f4795ae051089dcd8d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c952a48314207610c7b7b0a4853cbf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26abac73b9cb1af5c5d8e8c2dd136bbb.png)
A.![]() | B.![]() | C.2 | D.![]() |
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9卷引用:2019年广西柳州高中、南宁二中两校联考高三上学期第一次考试数学(理)试题
2019年广西柳州高中、南宁二中两校联考高三上学期第一次考试数学(理)试题河北省正定中学(实验中学)2019-2020学年高三下学期第三次阶段质量检测数学(理)试题北京市第八十中学2023-2024学年高一下学期3月阶段测试数学试题(已下线)模块五 专题六 全真拔高模拟2(已下线)模块五 专题6 全真拔高模拟2(北师版高一期中)湖南省衡阳市衡阳县第一中学2024届高三下学期4月月考数学试题宁夏回族自治区石嘴山市第一中学2023-2024学年高一下学期5月期中数学试题辽宁省东北育才学校科学高中部2023-2024学年高一下学期期中考试数学试题(已下线)专题05解三角形压轴小题归类(2) -期末考点大串讲(苏教版(2019))
2 . 已知有限数列
,从数列
中选取第
项、第
项、
、第
项(
),顺次排列构成数列
,其中
,
,则称新数列
为
的长度为m的子列.规定:数列
的任意一项都是
的长度为1的子列,若数列
的每一子列的所有项的和都不相同,则称数列
为完全数列.设数列
满足
,
.
(1)判断下面数列
的两个子列是否为完全数列,并说明由;
数列①:3,5,7,9,11;数列②:2,4,8,16.
(2)数列
的子列
长度为m,且
为完全数列,证明:m的最大值为6;
(3)数列
的子列
长度
,且
为完全数列,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5f59bc23cf55f56312c9ed9806371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af9e7b1c23db5584ad8521d4444d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608d034715f9b1dfb306f9c89d383582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0844d2b5218031f4a67807468b02653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbbc5edce52f4dda4f11770c4473f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a236fe66ea4ef97f3cba08affdb9de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a7c251895e500fb90228b3f366b66a2.png)
(1)判断下面数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
数列①:3,5,7,9,11;数列②:2,4,8,16.
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7a1d739890a8951586e23b78b035bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f41fc59006b724f49e63b64a413add.png)
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7卷引用:北京市昌平区2020届高三第二次统一练习(二模)数学试题
北京市昌平区2020届高三第二次统一练习(二模)数学试题(已下线)重难点1 数列-2021年高考数学【热点·重点·难点】专练(山东专用)北京中央民族大学附属中学2023届高三零模数学试题(已下线)北京市中央民族大学附属中学2023届高三零模数学试题北京市海淀外国语实验学校2023届高三三模检测数学试题北京市中关村中学2024届高三上学期9月开学考试数学试题(已下线)重难点10 数列的通项、求和及综合应用【九大题型】
3 . 已知集合
={x|x=a3×30+a2×3﹣1+a1×3﹣2+a0×3﹣3},其中ak∈{0,1,2},k=0,1,2,3,将集合
中的元素从小到大排列得到数列{bn},设{bn}的前n项和为Sn,则b3=_________________ ,S15=_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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名校
解题方法
4 . 设
是集合
且
中所有的数从小到大排列成的数列,即
,
,
,
,
,
,….
(1)写出集合
中
,
的所有的数;
(2)求
;
(3)
的前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7021e09bcc4e9d991c3f8ec4bcde057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35102ccb5f3b39e5a6c44076a0ff3fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8c45e4c4ab30665338dd87a2258f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d046ec9d9aaac508a16462f2980ca18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7abe2dbf91b745e81aa97bee35b0bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf86d176e66c7defe5a2543108e0769.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15a13b4190ac3d5feaee27a4c97b21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a495c197fcbacb8c109aa0060525a371.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfce7a88a7bf35de6a85fb20b56be8a.png)
(3)
![](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/81266597d1773b382659aa0b39fac710.png)
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5 . 若有穷数列
满足
且对任意的
,
至少有一个是数列
中的项,则称数列
具有性质![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断数列1,2,4,8是否具有性质P,并说明理由;
(2)设项数为
的数列
具有性质
,求证:
;
(3)若项数为
的数列
具有性质
,写出一个当
时,
不是等差数列的例子,并证明当
时,数列
是等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b96f565b4ca625ab41a782e3dfd0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0492686dc1959ba361d9b2832491620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e72ad2e72453867d089770c3f4c63da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断数列1,2,4,8是否具有性质P,并说明理由;
(2)设项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3411ddca520e2bcb516d0c5c0832aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee349b3f104aa5a5e03830a205570f3.png)
(3)若项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3411ddca520e2bcb516d0c5c0832aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0266e0e890fb1b84be352fdc65bb298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2020-12-25更新
|
586次组卷
|
6卷引用:重难点01 数列(基本通项求法)-2021年高考数学【热点·重点·难点】专练(上海专用)
(已下线)重难点01 数列(基本通项求法)-2021年高考数学【热点·重点·难点】专练(上海专用)北京市第五十五中学2022-2023年高二下学期3月调研数学试题上海市嘉定区2021届高三上学期一模数学试题(已下线)考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)专题05 《数列》中的解答题压轴题(2)-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)(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)
名校
6 . 对于实数数列{an},记
.
(1)若m1=1,m2=2,m3=4,m4=8,写出a1,a2,a3,a4的值;
(2)若数列{an}是等差数列,求证:对任意三元数组(i,j,k)(i,j,k两两不相等),总有(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=0;
(3)若对任意三元数组(i,j,k)(i,j,k两两不相等),存在常数c,使得(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=c,求证:{an}是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60c8c44a5521e7ef60131c4c3808091.png)
(1)若m1=1,m2=2,m3=4,m4=8,写出a1,a2,a3,a4的值;
(2)若数列{an}是等差数列,求证:对任意三元数组(i,j,k)(i,j,k两两不相等),总有(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=0;
(3)若对任意三元数组(i,j,k)(i,j,k两两不相等),存在常数c,使得(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=c,求证:{an}是等差数列.
您最近一年使用:0次
2020-12-21更新
|
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3卷引用:北京市密云区2021届高三上学期期中数学试题
名校
7 . 已知
是无穷数列,
,
且对于
中任意两项
,
在
中都存在一项
,使得
.
(1)若
,
求
;
(2)若
,求证:数列
中有无穷多项为
;
(3)若
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0361c11b97dbd249aaf084e8e8bb75fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0ad085279d897f162504ca5618608a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a4f4b1af1618089ebf0d32026f40dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0616dca5cf0229b9f801365cc2bcfff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba50a82a53f0e597c096ccf5746f1b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53abaaac2e62f510d996e6db22aefe7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f273c5e859fd6256f887c979bb78d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次
2020-11-15更新
|
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4卷引用:北京市海淀区2021届高三上学期期中考数学试题
北京市海淀区2021届高三上学期期中考数学试题北京一零一中学2022届高三9月月考统练一数学试题北京市第二十中学2022-2023学年高二下学期期中考试试卷(已下线)2020年高考北京数学高考真题变式题16-21题
8 . 已知数列
是无穷数列,其前n项和为
若对任意的正整数
,存在正整数
,
(
)使得
,则称数列
是“S数列".
(1)若
判断数列
是否是“S数列”,并说明理由;
(2)设无穷数列
的前n项和
且
,证明数列
不是“S数列";
(3)证明:对任意的无穷等差数列
,存在两个“S数列"
和
,使得
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a60fab9ac1eb590b1e3a9b1567f570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd52cb7d9da16f9b684819aca74c8de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467295c3a236b7e41b84812a3f74d929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c399549ad8bbdec1e659450fbd13d8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b6941b6c2e6767973a16227705c7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5029180d358fd5c6957bef63623eedec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)证明:对任意的无穷等差数列
![](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/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c9572319e55d5eb64cc037ab740956.png)
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名校
9 . 已知数列
的前n项和
满足
,且
,数列
满足
,
,其前9项和为36.
(1)当n为奇数时,将
放在
的前面一项的位置上;当n为偶数时,将
放在
前面一项的位置上,可以得到一个新的数列:
,
,
,
,
,
,
,
,
,
,…,求该数列的前n项和
;
(2)设
,对于任意给定的正整数
,是否存在正整数l、
,使得
、
、
成等差数列?若存在,求出l、m(用k表示),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/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0f680ecbd480ae093a9d72e4b8b594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0108d4f0f000137d846363ee63b7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37bd079cf3329af20b2609b08c9f8c4.png)
(1)当n为奇数时,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066b52c4c6c26644547d8e3542510529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0505b3b01eabf49fa1cd907fe92deb03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12232f27c4c46676efbb0247256cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c26ec59a4f997e03ab1d9345eec4b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829442c6473c94fde041595bc18530d7.png)
您最近一年使用:0次
2020-08-14更新
|
599次组卷
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5卷引用:上海市实验学校2019-2020学年高一下学期期末数学试题
上海市实验学校2019-2020学年高一下学期期末数学试题2023年普通高等学校招生全国统一考试模拟(北京卷)数学试题苏教版(2019) 选修第一册 一蹴而就 第4章 单元整合(已下线)专题17 数列探索型、存在型问题的解法 微点3 数列探索型、存在型问题综合训练(已下线)重难点03:数列近3年高考真题赏析-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)
名校
解题方法
10 . 设数列:A:a1,a2,…,an,B:b1,b2,…,bn.已知ai,bj∈{0,1}(i=1,2,…,n;j=1,2,…,n),定义n×n数表
,其中xij
.
(1)若A:1,1,1,0,B:0,1,0,0,写出X(A,B);
(2)若A,B是不同的数列,求证:n×n数表X(A,B)满足“xij=xji(i=1,2,…,n;j=1,2,…,n;i
j)”的充分必要条件为“ak+bk=1(k=1,2,…,n)”;
(3)若数列A与B中的1共有n个,求证:n×n数表X(A,B)中1的个数不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d80a140f78215fd78b28b2f056621b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07de86b00421ff253924b24f15b7047.png)
(1)若A:1,1,1,0,B:0,1,0,0,写出X(A,B);
(2)若A,B是不同的数列,求证:n×n数表X(A,B)满足“xij=xji(i=1,2,…,n;j=1,2,…,n;i
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411837b4b3078d05b43cb0439259a362.png)
(3)若数列A与B中的1共有n个,求证:n×n数表X(A,B)中1的个数不大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c863b250e389c3992dd27963a0b78900.png)
您最近一年使用:0次
2020-06-22更新
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621次组卷
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3卷引用:北京市东城区2020届高三第二学期二模考试数学试题