1 . 几位大学生响应国家的创业号召,开发了一款应用软件.为激发大家学习数学的兴趣,他们推出了“解数学题获取软件激活码”的活动.这款软件的激活码为下面数学问题的答案:已知数列1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,…,其中第一项是
,接下来的两项是
,
,再接下来的三项是
,
,
,依此类推.求满足如下条件的最小整数N:
且该数列的前N项和为2的整数幂.那么该款软件的激活码是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ad4668cc927e277289b2af718f0d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c851ab8c7c8b2ac92092987a7e32493f.png)
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2022-09-14更新
|
1155次组卷
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10卷引用:上海市大同中学2017-2018学年高三上学期10月月考数学试题
上海市大同中学2017-2018学年高三上学期10月月考数学试题(已下线)2019年上海市华东师范大学第二附属中学高三下学期5月信心考三模数学试题2020届湖南省长沙市长郡中学高三上学期第5次月考数学(文)试题2020届湖南省长沙市长郡中学高三第五次月考数学(文)试题辽宁省渤海大学附属高级中学2022-2023学年高三上学期第二次月考数学试题(已下线)专题17 数列(模拟练)福建师范大学附属中学2023届高三上学期第二次月考数学试题四川省成都市锦江区嘉祥外国语高级中学2022-2023学年高二上学期入学考试数学试题(已下线)第三节 等比数列 核心考点集训2024年新高考Ⅰ卷浙大优学靶向精准模拟数学试题(二)
2 . 已知公差d不为0的等差数列
的前n项和为
,
,
.
(1)求数列
的通项公式;
(2)若数列
,
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8c45e4c4ab30665338dd87a2258f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4e32575d33b8a9979f4760afd361f9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d44ddab6e0c60119be69985ae7fa65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2022-08-30更新
|
1111次组卷
|
5卷引用:上海市建平中学2023届高三下学期3月月考数学试题
名校
3 . 已知复数列
满足:
,
,设复数
在复平面中对应点
.当
无限增大时,点
越来越趋近于一个确定的点
,点
的坐标是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c916fd7ddb4e800d98b15ce54c4d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2103a934a70ceb3f67525a1bfe9200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176f249595624605402d8cb1bcb4eae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176f249595624605402d8cb1bcb4eae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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4 . 已知数列
的通项公式为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc009e82148c32647621725edf12b44.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cb6d4197ddd283f33bc12d231a314b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc009e82148c32647621725edf12b44.png)
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5 . 甲、乙两人同时分别入职
两家公司,两家公司的基础工资标准分别为:
公司第一年月基础工资数为3700元,以后每年月基础工资比上一年月基础工资增加300元;
公司第一年月基础工资数为4000元,以后每年月基础工资都是上一年的月基础工资的1.05倍.
(1)分别求甲、乙两人工作满10年的基础工资收入总量(精确到1元)
(2)设甲、乙两人入职第
年的月基础工资分别为
、
元,记
,讨论数列
的单调性,指出哪年起到哪年止相同年份甲的月基础工资高于乙的月基础工资,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)分别求甲、乙两人工作满10年的基础工资收入总量(精确到1元)
(2)设甲、乙两人入职第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](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/831de7531e4b51f836a5ef44c4791198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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2022-06-23更新
|
1801次组卷
|
12卷引用:上海市曹杨第二中学2022-2023学年高二上学期10月月考数学试题
上海市曹杨第二中学2022-2023学年高二上学期10月月考数学试题上海市闵行区闵行中学2024届高三上学期12月月考数学试题上海市青浦高级中学2023-2024学年高二下学期3月质量检测数学试卷上海市长宁区2022届高考二模数学试题上海师范大学附属中学2022-2023学年高二上学期期中数学试题上海市上海交通大学附属中学2022-2023学年高三上学期期中考试数学试题(已下线)专题19 数列的综合应用-2(已下线)考向19等差数列及其前n项和(重点)-2(已下线)第08讲 等差、等比数列-2(已下线)专题06数列必考题型分类训练-3(已下线)数列求和(已下线)专题19 数列应用题的解法 微点2 数列应用题综合训练
6 . 设复数数列
满足:
,且对任意正整数n,均有:
.若复数
对应复平面的点为
,O为坐标原点.
(1)求
的面积;
(2)求
;
(3)证明:对任意正整数m,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b670aca396b96eaf2c553b1ca84486dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a383b03b4869ea984d58b8d87c35402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012d2d40a71783e79d67e7fbb01bc93a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8312ce4d9e9f0aff13e64d93fbea921e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5927f1967a8f72e8fb887edb5023a921.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fec8f8ce956e4621c34db6218ed072.png)
(3)证明:对任意正整数m,均有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea99696f6df9d98c2dcc87832002874.png)
您最近一年使用:0次
名校
解题方法
7 . 已知无穷数列
满足
.其中
、
均为非负实数且不同时为
.
(1)若
,
,且
,求
的值;
(2)若
,
,求数列
的前
项和
;
(3)若
,
,求证:当
时,数列
是单调递减数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dffb9c81395b0af0ff6218c34659574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06699d84ba9a594d21ba1585fe1f340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4393a1d553fd7c8beae61d72679f56b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96a231949c975db546185f61f8a4571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4663e5f34de1f155c3320dc51488ec62.png)
![](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)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7dff298384b52ac8cd9a2fc167e7b7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3982b8d0a6dea50b0c4778bcf196450a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
8 . 已知无穷数列
满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cee45170ef38fc988fd04d1e223d94.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ab9227bed2c841dfb7dddbbec4020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cee45170ef38fc988fd04d1e223d94.png)
您最近一年使用:0次
2022-04-26更新
|
471次组卷
|
4卷引用:上海市宝山区上海师大附属宝山罗店中学2023-2024学年高二下学期第一次诊断性测试(3月)数学试卷
上海市宝山区上海师大附属宝山罗店中学2023-2024学年高二下学期第一次诊断性测试(3月)数学试卷上海交通大学附属中学2021-2022学年高二下学期期中数学试题(已下线)4.2无穷等比数列各项和(第3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)上海市黄浦区2022-2023学年高二下学期期末数学试题
名校
9 . 设数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46caae83a3d839b68c8b1153093b340c.png)
__________ .
![](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/20ef7fade67001f9d4f7825857c17567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46caae83a3d839b68c8b1153093b340c.png)
您最近一年使用:0次
名校
解题方法
10 . 设自然数
,若由n个不同的正整数
,
,…,
构成的集合
满足:对集合S的任何两个不同的非空子集A、B,A中所有元素之和与B中所有元素之和均不相等,则称集合S具有性质P.
(1)试分别判断在集合
与
是否具有性质P,不必说明理由;
(2)已知集合
具有性质P.
①记
,求证:对于任意正整数
,都有
;
②令
,
,求证:
;
(3)在(2)的条件下,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.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/192fc415cb8db504ffb1ad939981b7a2.png)
(1)试分别判断在集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869ae0235255b84ece86c8bd81939067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc5cbe002e669214c4c1597bc8b0caf.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192fc415cb8db504ffb1ad939981b7a2.png)
①记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31295a254d093889374c947aa881a308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b4b3879d1c6debf0333008f686634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87270dc51105d272c6f76af461d08457.png)
②令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e9ca7e90d47d7ee295338bbac2d8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa81f4cef9531213df1b3261295508eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1557d3b215f58330d34827b134ad2925.png)
(3)在(2)的条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749877d42d1984fb42369b7bb4e376c7.png)
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