1 . 已知数列
是以
为首项,
为公差的等差数列;
是以
为首项,
为公比的等比数列,设
,
,则下列结论正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000f01319364c59dee948848fc4de4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39fe4fa6a03e969e339f9c1812ef633.png)
A.![]() | B.![]() |
C.![]() | D.若![]() ![]() ![]() |
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|
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2卷引用:山东省青岛市莱西市2021-2022学年高二上学期期末数学试题
名校
解题方法
2 . 已知数列
的前n项和为
,且
,
,
为等差数列;数列
满足
,
.
(1)求数列
的前n项和
;
(2)若对于
,总有
成立,求实数m的取值范围.
![](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/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a8d7ec3afb812286ad33dd69d80c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d26750bec2579005dc35313767ec68d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)若对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33174d336af6648b9303c49858937b41.png)
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965次组卷
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4卷引用:山东省青岛市莱西市2021-2022学年高三上学期期末数学试题
山东省青岛市莱西市2021-2022学年高三上学期期末数学试题(已下线)第17节 等比数列及前n项和宁夏回族自治区石嘴山市第三中学2023-2024学年高三上学期期末考试理科数学试题(已下线)专题05 数列 第三讲 数列与不等关系(分层练)
名校
解题方法
3 . 已知欧拉函数
的函数值等于所有不超过正整数
,且与
互素的正整数的个数.例如:
,
,设数列
中:
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807ff2f0a7bf0514032911551bf8654f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edd29e22f6a7f4d14d9f8d2684d47e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39de1bc04496b97dcf401c669e6ab44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e1442a2d46f09dcc17dc920805afe4.png)
A.数列![]() |
B.![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
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6卷引用:山东省临沂第十九中学2022-2023学年高二上学期期中考试数学试题
山东省临沂第十九中学2022-2023学年高二上学期期中考试数学试题重庆市巴蜀中学2021-2022学年高二上学期期末数学试题(已下线)第4章 数列(新文化30题专练)2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)4.1数列(第2课时)(分层作业)(2)(已下线)第六篇 数论 专题2 数论函数 微点2 欧拉函数与Mobius函数云南省保山市腾冲市第八中学2023-2024学年高二上学期期末模拟数学试题
名校
4 . 已知等差数列
的前
项和为
,
,公差
,
.若
取得最大值,则
的值为( )
![](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/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8bbb4a09e0ac86bbae46222a90841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa7b5c3f38bcfeb252e2b9183145e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.6或7 | B.7或8 | C.8或9 | D.9或10 |
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7卷引用:山东省青岛市4区市2021-2022学年高二上学期期中考试数学试题
山东省青岛市4区市2021-2022学年高二上学期期中考试数学试题(已下线)2020年高考北京数学高考真题变式题6-10题吉林省长春吉大附中实验学校2021-2022学年高二上学期期末数学试题浙江省金华市义乌市商城学校2021-2022学年高二上学期12月月考数学试题(已下线)第01讲 数列的概念与简单表示法 (精讲)-3江苏省扬州市高邮市第一中学2022-2023学年高二上学期期中热身数学试题重庆市两江育才中学校2022-2023学年高二上学期期末数学试题
5 . 如图的形状出现在南宋数学家杨辉所著的《详解九章算法·商功》中,后人称为“三角垛”.“三角垛”最上层有
个球,第二层有
个球,第三层有
个球,….设第
层有
个球,从上往下
层球的总数为
,记
,则( )
![](https://img.xkw.com/dksih/QBM/2021/11/17/2853314574753792/2857251206635520/STEM/d19f1e30498d476ab4c509760547c07c.png?resizew=91)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7e3a488821215128f15ef8707f7847.png)
![](https://img.xkw.com/dksih/QBM/2021/11/17/2853314574753792/2857251206635520/STEM/d19f1e30498d476ab4c509760547c07c.png?resizew=91)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
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965次组卷
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4卷引用:山东省青岛市4区市2021-2022学年高二上学期期中考试数学试题
名校
解题方法
6 . 已知数列
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dac541885bc227cd97fb148ca7c3f93.png)
A.此数列没有最大项 | B.此数列的最大项是![]() |
C.此数列没有最小项 | D.此数列的最小项是![]() |
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8卷引用:山东省枣庄市滕州市第一中学2021-2022学年高三上学期期中数学试题
山东省枣庄市滕州市第一中学2021-2022学年高三上学期期中数学试题山东省枣庄市滕州市2021-2022学年高三上学期期中数学试题(已下线)2020年高考北京数学高考真题变式题6-10题山西省怀仁市第一中学2021-2022学年高二上学期期末数学(文)试题(已下线)易错点08 数列-备战2022年高考数学考试易错题(新高考专用)(已下线)4.1数列的概念B卷(已下线)专题23 数列的基本知识与概念 -1第四章 数列(单元测)
名校
7 . 已知数列
的通项公式
,记
为数列
的前
项和,若使
取得最小值,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a75245f0bac7d50f695c768b34e6ce3.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
A.5 | B.5或6 | C.10 | D.9或10 |
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4卷引用:山东省潍坊市昌乐县北大公学学校2024届高三上学期第一次月清数学试题
解题方法
8 .
为平面直角坐标系
的坐标原点,点
.在
轴正半轴上依次取
中点
,
中点
,
中点
,…,
中点
,…记
,
.则(1)数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
___________ ;(2)记
,数列
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eada9cfc38cb9fc560dc84e045837993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3225a61541f2cbe6f47de8138f6c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b8405d5bc106650918899daa9a7818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc80881005ad413aa53744238cdc83b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b6dcb0c6c8ba3ab5924baff8ec1c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626366ae67d79e98b405f9d1adfd08b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385bfd963a8568e4ddb264497ed61782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273711167f15858b9992a69ed5b65b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3a44a5aecf68dff7a81bd60212a2e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
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9 . 设正项数列
的前
项之和
,数列
的前
项之积
,且
.
(1)求证:
为等差数列,并分别求
、
的通项公式;
(2)设数列
的前
项和为
,不等式
对任意正整数
恒成立,求正实数
的取值范围.
![](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/9b425d344cf967570ef9d9a3c53ad4d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdee207ed0aaf87c78a1fba1566042b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5175f3097ba91a11fc64feb1f272c1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c83451624b13a97e0abf0f4a9b46f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea78d8e044bfada5b4c6cf44ea2a8d5.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/623174058f4dd7204d3a919a191bfa03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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|
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5卷引用:山东省济南市山东师范大学附属中学2022-2023学年高三下学期3月月考数学试题
10 . 已知等差数列
的前n项和为
,公差为
,
,
,当
取最小值时,n的值为( )
![](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/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6452c7f7b8afad5557869613cf05e12f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e210e2af059651ec783ab5d33a4fe34.png)
A.7 | B.8 | C.9 | D.10 |
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5卷引用:山东省2021年普通高等学校招生全国统一考试模拟数学试题
山东省2021年普通高等学校招生全国统一考试模拟数学试题山东省泰安市2021届高三四模数学试题(已下线)考点15 等差数列及其前n项和-备战2022年高考数学(理)一轮复习考点微专题(已下线)第16题 数列求和-2021年高考数学真题逐题揭秘与以例及类(新高考全国Ⅰ卷)(已下线)专题04 数列(突破训练)-备战2022年高考数学二轮复习重难考点专项突破训练(全国通用)