真题
1 . 已知
,
,
不为常数列且各项均不相同,下列正确的是______ .
①
,
均为等差数列,则M中最多一个元素;
②
,
均为等比数列,则M中最多三个元素;
③
为等差数列,
为等比数列,则M中最多三个元素;
④
单调递增,
单调递减,则M中最多一个元素.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0039bbb7d9faa2356950ef536ec7d7b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
2 . 已知数列
各项均为正数,其前n项和
满足
.给出下列四个结论:
①
的第2项小于3; ②
为等比数列;
③
为递减数列; ④
中存在小于
的项.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e783576b8e6b542394e48531ac04b419.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
③
![](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/6bfdaa01ae7652656f1f0ccad1a2149c.png)
其中所有正确结论的序号是
您最近一年使用:0次
2022-06-07更新
|
14713次组卷
|
30卷引用:2022年新高考北京数学高考真题
2022年新高考北京数学高考真题北京市第十三中学2023届高三上学期开学考试数学测试题北京市第二十二中学2023届高三上学期开学考试数学试题(已下线)重组卷05北京市石景山区2022-2023学年高二下学期期末考试数学试题北京十年真题专题06数列【北京专用】专题01数列(第一部分)-高二上学期名校期末好题汇编(已下线)2022年新高考北京数学高考真题变式题5-8题福建省厦门外国语学校2021-2022学年高二下学期数学期末模拟试题(4)(已下线)专题06 数列(文理)(已下线)考点6-3 数列通项与递推公式综合应用(文理)-2023年高考数学一轮复习小题多维练(全国通用)(已下线)第01讲 数列的概念与简单表示法(练)(已下线)2022年新高考北京数学高考真题变式题13-15题(已下线)专题5 2022年高考“数列”专题命题分析(已下线)第95练 计算速度训练15(已下线)重组卷04(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-1上海市向明中学2024届高三上学期开学考试数学试题(已下线)第01讲 数列的基本知识与概念(练习)黑龙江省哈尔滨市第七十三中学校2024届高三上学期期中数学试题人教A版(2019) 选修第二册 数学奇书 选修第二册 模块综合检测卷(一)(已下线)考点6 等比数列的前n项和的性质 2024届高考数学考点总动员(已下线)等差数列与等比数列(已下线)第4讲:数列中的最值问题【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)(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)技巧02 填空题的答题技巧(8大题型)(练习)(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)专题06 数列小题(理科)-1(已下线)专题05 数列小题(7类题型,文科)
3 . 设p为实数.若无穷数列满足如下三个性质,则称
为
数列:
①,且
;
②;
③,
.
![](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/3be16c2cf7aae777e1b68354fe0b3543.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9d7c2eeebbf6d24c659dec05e7cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(3)设数列
![](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/b46cd00743394b0f8636c08fc6abc521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1391b1323ca839ae8bcc075f9387935f.png)
您最近一年使用:0次
2021-06-17更新
|
11741次组卷
|
19卷引用:2021年北京市高考数学试题
2021年北京市高考数学试题(已下线)重组卷01北京市密云区2023届高三考前保温练习(三模)数学试题北京市第一零九中学2023届高三高考冲刺数学试题北京十年真题专题06数列(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)课时25 数列新定义-2022年高考数学一轮复习小题多维练(上海专用)上海市上海师范大学附属中学2022届高三上学期期中数学试题(已下线)2021年新高考北京数学高考真题变式题16-21题上海市黄浦区大同中学2022届高三上学期12月月考数学试题(已下线)热点04 数列求和及综合应用-2022年高考数学【热点·重点·难点】专练(全国通用)(已下线)押新高考第18题 数列-备战2022年高考数学临考题号押题(新高考专用)(已下线)查补易混易错点04 数列-【查漏补缺】2022年高考数学三轮冲刺过关(新高考专用)上海市南洋模范中学2021-2022学年高三上学期12月月考数学试题(已下线)数列新定义湖北省黄冈市浠水县第一中学2024届高三下学期第一次高考模拟数学试题(已下线)黄金卷02(2024新题型)(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大核心考点)(讲义)河南省信阳市新县高级中学2024届高三考前第一次适应性考试数学试题
4 . 对于每项均是正整数的数列
,定义变换
将数列A变换成数列
.对于每项均是非负整数的数列
,定义变换
将数列B各项从大到小排列,然后去掉所有为零的项,得到数列
;又定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff9686b94826bacb9447d72aa59f496.png)
.设
是每项均为正整数的有穷数列,令
.
(1)如果数列
为5,3,2,写出数列
;
(2)对于每项均是正整数的有穷数列A,证明
;
(3)证明:对于任意给定的每项均为正整数的有穷数列
,存在正整数K,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ca40abb85f4e8c8971e7a1751be372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05725d689ad4c7f7c1af29ccaa21d5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f9e6a72e004b1b3c6f903b530be575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb60f7bb6b97c008d1b9235936e100a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703a1c5f9bc7d613496689a861bb0de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff9686b94826bacb9447d72aa59f496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ef999b54fac369aa3b9939d9e9ad61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1547922f21a55e6cf6d15f1492e544f6.png)
(1)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
(2)对于每项均是正整数的有穷数列A,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb314761684dddad5606738c67b790b.png)
(3)证明:对于任意给定的每项均为正整数的有穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b6ba2966874d33da6b94662d7cb23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291de980856351b0dd6582f33ab4d288.png)
您最近一年使用:0次
真题
5 . 数列
满足
是常数.
(1)当
时,求
及
的值;
(2)数列
是否可能为等差数列?若可能,求出它的通项公式;若不可能,说明理由;
(3)求
的取值范围,使得存在正整数m,当
时总有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7913d4ae473dad6671200d7cc577b3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562bf10d55724c77204c6953c7fbf7e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6a46c5fb744758ad83902819b83bbf.png)
您最近一年使用:0次
2022-11-12更新
|
651次组卷
|
3卷引用:2008年普通高等学校招生全国统一考试文科数学(北京卷)
6 . 给定数列
.对
,该数列前
项的最大值记为
,后
项
的最小值记为
,
.
(1)设数列
为
,
,
,
,写出
,
,
的值;
(2)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5b296e1144d0e0398332a72bee14ce.png)
是公比大于
的等比数列,且
.证明:
是等比数列.
(3)设
是公差大于
的等差数列,且
,证明:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5b296e1144d0e0398332a72bee14ce.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285100347392/1571285106163712/STEM/632e2f6ad38946709a1e99b3670154c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7ae03cc5b86e350a8d81db0d6b473b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac5f5fc996af5eb8f6619bc124e4d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc5c895153932c3e827a464664cef90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6aaf7040d41361eb30084796264d65.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d0252c1b2f7d2a84b5c985d19d547.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5b296e1144d0e0398332a72bee14ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3492fed4c32f003868cf173a2e9085e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d157b8c366da862bb263221f2c566f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e81bc3cb9f0327445ac9be85c20f4c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e81bc3cb9f0327445ac9be85c20f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fa462125a76ef6776c05c7aa2bc464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ef10ef2b181375883e3fe8c9ce7a56.png)
您最近一年使用:0次
2019-01-30更新
|
2199次组卷
|
7卷引用:2013年全国普通高等学校招生统一考试文科数学(北京卷)
7 . 设数列A:
,
,…
(
).如果对小于
(
)的每个正整数
都有
<
,则称
是数列A的一个“G时刻”.记“
是数列A的所有“G时刻”组成的集合.
(1)对数列A:-2,2,-1,1,3,写出
的所有元素;
(2)证明:若数列A中存在
使得
>
,则
;
(3)证明:若数列A满足
-
≤1(n=2,3, …,N),则
的元素个数不小于
-
.
![](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/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b1ddacf11a9a5ab29fd966f55c580c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5059e492214c793847f8a11dffff0b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f596794823f3b08582f99f0047e880.png)
(1)对数列A:-2,2,-1,1,3,写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f596794823f3b08582f99f0047e880.png)
(2)证明:若数列A中存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.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/be1ade4d9652e39fc8b604a58dd6453e.png)
(3)证明:若数列A满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7230de53663c75658c58bbf206a0085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f596794823f3b08582f99f0047e880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
2016-12-04更新
|
3271次组卷
|
22卷引用:2016年全国普通高等学校招生统一考试理科数学(北京卷精编版)
2016年全国普通高等学校招生统一考试理科数学(北京卷精编版)(已下线)2016年全国普通高等学校招生统一考试理科数学(北京卷参考版)北京市西城区北京师范大学第二附属中学2019-2020学年高三上学期期中数学试题北京市第十三中学2021届高三上学期期中考试数学试题北京第五十七中学2020-2021学年高二上学期期末试题北京师范大学第三附属中学2022届高三下学期5月模拟练习数学试题北京师范大学第三附属中学2022届高三下学期5月高考数学模拟试题北京市玉渊潭中学2023届高三下学期开学摸底数学试题北京市育英学校2023届高三6月统一练习(一) 数学试题北京市育英学校(四年制高三)2021-2022学年高二下学期期中练习数学试题北京十年真题专题06数列(已下线)《2018届优等生百日闯关系列》【江苏版】专题二 第五关 以子数列或生成数列为背景的解答题(已下线)《2018届优等生百日闯关系列》【江苏版】专题二 第六关 以新定义数列为背景的解答题上海市曹杨二中2018-2019学年高三上学期期末数学试题上海市市东中学2016-2017学年高三下学期第一次测验数学试题(已下线)专题14 数列综合-五年(2016-2020)高考数学(文)真题分项(已下线)考点17 数列的综合运用-备战2022年高考数学(理)一轮复习考点微专题上海实验学校2022届高三冲刺模拟4数学试题北京名校2023届高三二轮复习 专题三 集合与数列 第4讲 创新自我测试(已下线)专题16 数列新定义题的解法 微点2 数列新定义题的解法(二)(已下线)数列的综合应用(已下线)专题21 数列解答题(理科)-2
真题
名校
8 . 已知数列
满足:
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8094aae498aec981ce621a032007ce26.png)
.记
集合
.
(Ⅰ)若
,写出集合
的所有元素;
(Ⅱ)若集合
存在一个元素是3的倍数,证明:
的所有元素都是3的倍数;
(Ⅲ)求集合
的元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87397e6df8ed820638eea31e403a94b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69552a67ba83e9c4a70901a5d49a8519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8094aae498aec981ce621a032007ce26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a765bfd025a46459618f5ef76321696a.png)
集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21550abb7c545b53cd2336a7a76885fb.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecf69901899bba130968c7a091790d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅱ)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅲ)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2016-12-03更新
|
3067次组卷
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12卷引用:2015年全国普通高等学校招生统一考试理科数学(北京卷)
9 . 对于数对序列
,记
,
,其中
表示
和
两个数中最大的数.
(1)对于数对序列
,求
的值;
(2)记
为
,
,
,
四个数中最小的数,对于由两个数对
组成的数对序列
和
,试分别对
和
两种情况比较
和
的大小;
(3)在由五个数对
组成的所有数对序列中,写出一个数对序列
使
最小,并写出
的值.(只需写出结论).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2736ab1e167069b9a47df848a996dcc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8834ee942195016dac04b95b02bcee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9560b3d0a8aaead5cfb6b642c1720dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c49f2f0a3224a996d19d762f20ca4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9edd142f74210ba622467c0a0b9792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c1352a409a961fe422dc48dadc6f8f.png)
(1)对于数对序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26dbaec32ca88e667627df9c474c731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9af9757ccb5f4f283dc841e6fdfec8.png)
(2)记
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782625320960/1571782631096320/STEM/13ba3952c3da428fa05dbb913bfb19f5.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782625320960/1571782631096320/STEM/4a26d96f05a348a1b1141ac618ae6510.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782625320960/1571782631096320/STEM/04545854afd846979e9728d36880a3dc.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782625320960/1571782631096320/STEM/7b73015078b348069640993b00ee79c7.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782625320960/1571782631096320/STEM/5d8473eb22d8426db0698598707eac5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e80e51bbddab5d1b0c8c46a6ca3dc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e62660939c66c2fadbaacc3cb5bfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ecc7216602d000e1b0c8131c1153c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e631eb268821e9cb3c1b8ad50801594c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bd86b38966808a65534668e39a14b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da611e4f6af389a0e0a2227201eae346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6337bad2b5cc25d9af7b29c3dfc1df38.png)
(3)在由五个数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1203c18a8e3303939b1f541690a3549.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782625320960/1571782631096320/STEM/9e366206df924d25af94033222bd9898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a5c714c427da0a7d2b2f2db68edb9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a5c714c427da0a7d2b2f2db68edb9c.png)
您最近一年使用:0次
2016-12-03更新
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3736次组卷
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7卷引用:2014年全国普通高等学校招生统一考试理科数学(北京卷)
10 . 已知数集
具有性质
;对任意的
,
与
两数中至少有一个属于
.
(Ⅰ)分别判断数集
与
是否具有性质
,并说明理由;
(Ⅱ)证明:
,且
;
(Ⅲ)证明:当
时,
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d228c2d9c8929a1e02da010ba2f82552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669bb38ce88af69eb805246c960166e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f52783e7a39f438adf08ef7d05d8c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf9fc9e8c9940547678ff7934363f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅰ)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0547b8e498e87af46afcc1b983b7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b7e018b11b0e2b938ac8c12cee68ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e1582eea740e7451295b3f23ac76c93.png)
(Ⅲ)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569627575492608/1569627633090560/STEM/e394d64b64284a55a5b41e1000802016.png)
您最近一年使用:0次
2016-11-30更新
|
408次组卷
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6卷引用:2009年普通高等学校招生全国统一考试理科数学(北京卷)