1 . 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)
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解题方法
2 . 已知
是等比数列,
,公比
,若
.
(1)求k的值;
(2)设
是
的前n项和,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90317672df8cb902a3344004f0f916c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e3fc803117ae94861839984a0afef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fc0397dbfde6611cd52abb102b01a.png)
(1)求k的值;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f90c472b3cbcd1da548cad9db5455c.png)
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21-22高二下·上海浦东新·期中
名校
3 . 在等差数列
和等比数列
中,
,
,
是数列
前n项和.
(1)求
;
(2)若
,求证:“数列
的所有项都在数列
中”的充要条件为“b为正偶数”;
(3)是否存在正实数b,使得数列
中至少有三项在数列
中,但
中的项不都在数列
中?若存在,求出一个可能的b的值;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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5a7a17a394e868e0acd1803a9ab795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe8b3668a8c01835ce26100945097e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c387f6838405f1bf06fd2c74b3a31481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)是否存在正实数b,使得数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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4 . 已知等差数列
的前
项和为
,
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](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/680ef2ef49520b67528bfadd91b3706c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9253eb4b892b8ae34fd6baf4b02460d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2022-04-12更新
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6092次组卷
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10卷引用:上海市洋泾中学2022-2023学年高二上学期期中数学试题
上海市洋泾中学2022-2023学年高二上学期期中数学试题广东省佛山市十五校2021-2022学年高二下学期期中联考数学试题(已下线)第04讲 数列求和 (高频考点—精讲)-2(已下线)专题12 数列大题专项训练浙江省湖州市长兴县、德清县,安吉县等三县2017-2018学年高一下学期期中数学试题吉林省吉林市田家炳高级中学2022-2023学年高二上学期期末数学试题(已下线)4.3.2 等比数列的前n项和公式(第1课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)江西省南昌市江西科技学院附属中学2022-2023学年高二下学期3月月考数学试题贵州省黔西南州2022-2023学年高二下学期期末教学质量检测数学试题四川省遂宁市射洪中学校2023-2024学年高二上学期第三次学月考试数学试题
5 . 已知数列
通项公式
,求数列
的前n项和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d360b1520d2e784c5e85611139583950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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名校
解题方法
6 . 某病毒研究所为了更好地研究“新冠”病毒,计划改建十个实验室,每个实验室的改建费用分为装修费和设备费,每个实验室的装修费都一样,设备费从第一到第十实验室依次构成等比数列,已知第五实验室比第二实验室的改建费用高28万元,第七实验室比第四实验室的改建费用高112万元,并要求每个实验室改建费用不能超过1100万元.则该研究所改建这十个实验室投入的总费用最多需要( )
A.2806万元 | B.2906万元 | C.3106万元 | D.3206万元 |
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2022-03-17更新
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883次组卷
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5卷引用:上海市上海中学东校2021-2022学年高一下学期期末数学试题
上海市上海中学东校2021-2022学年高一下学期期末数学试题云南省昭通一中等三校2022届高三下学期高考备考实用性联考(四)数学(文)试题(已下线)专题04 数列的通项、求和及综合应用(精讲精练)-3(已下线)专题16 数学实际应用题江西省彭泽县第二高级中学2022-2023学年高二下学期7月期末数学试题
7 . 如图,已知点D为
的边
上一点,
,
为
边上一列点,满足
,其中数列
满足
,
,
,则
的所有项的和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c8df1c05e4bd7e8af29480e8fc299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a5473e97ea227cdb8767dcde0a9bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb2226a6dd77f1f851e010bc5fd74e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5aa4c0745a3ff5f4889b6fd711bc442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://img.xkw.com/dksih/QBM/2022/3/4/2929135900196864/2932374487711744/STEM/d465e971e5ff43ce9850aaf8ec73c7be.png?resizew=232)
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8 . 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)
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解题方法
9 . “康托尔尘埃”是数学理性思维的构造产物,具有典型的分形特征,其操作过程如下:在一个单位正方形中,首先,将正方形等分成
个边长为
的小正方形,保留靠角的
个小正方形,记
个小正方形的面积和为
;然后,将剩余的
个小正方形分别继续
等分,分别保留靠角的
个小正方形,记所得的
个小正方形的面积和为
;……;操作过程不断地进行下去,以至无穷,保留的图形称为康托尔尘埃.若
,则需要操作的次数
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad607f4fa8d42c9d0bf3c694243b91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2021/8/20/2790333436444672/2795293842759680/STEM/984dd5938e3f4473a977bb0c31ff4847.png?resizew=149)
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2021-08-27更新
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624次组卷
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5卷引用: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
上海师范大学附属中学2022-2023学年高二上学期期中数学试题(已下线)考点10 等比数列-2022年高考数学一轮复习小题多维练(新高考版)2023版 苏教版(2019) 选修第一册 名师精选卷 第四章 数列江苏省盐城市2022-2023学年高三上学期12月初调研考试数学试题贵州省贵阳市2022届高三摸底考试试卷数学(文)试题
10 . 在等比数列{an}中,公比q=2,前n项和为Sn,若S5=1,则S10=________ .
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2021-04-18更新
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7卷引用:上海市华东师范大学第二附属中学2022届高三下学期6月练习数学试题
(已下线)上海市华东师范大学第二附属中学2022届高三下学期6月练习数学试题沪教版(2020) 选修第一册 领航者 第4章 4.2 第3课时 等比数列的前n项和(1)沪教版 高二年级第一学期 领航者 第七章 7.3 等比数列(4)2018年上海市青浦区高三4月质量调研(二模)数学试题(已下线)4.3.2 等比数列的前n项和公式(第2课时)(练习)-2020-2021学年上学期高二数学同步精品课堂(新教材人教版选择性必修第二册)(已下线)专题05 等比数列的前n项和公式 核心素养练习 -【新教材精创】2020-2021学年高二数学新教材知识讲学(人教A版选择性必修第二册)(已下线)第4章 数列(基础、典型、易错、压轴)-【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)