1 . 已知无穷实数列
,
,若存在
,使得对任意
,
恒成立,则称
为有界数列;记
,若存在
,使得对任意
,
恒成立,则称
为有界变差数列.
(1)已知无穷数列
的通项公式为
,判断
是否为有界数列,是否为有界变差数列,并说明理由;
(2)已知首项为
,公比为实数
的等比数列
为有界变差数列,求
的取值范围;
(3)已知两个单调递增的无穷数列
和
都为有界数列,记
,
,证明:数列
为有界变差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3020838d53c5cf3e3ef3c323917ba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f49b4e00ea2c0bb4200795de17d426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094f977194228bed828f3507f5898934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c7aab4df25884973273efae244f2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5ba7e16abbfc05737699584023d4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(1)已知无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a026996f510aa79d5b308885a5b4dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)已知首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e1ee88beaddafb0d0a185c3a8e0dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)已知两个单调递增的无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11913c4302df9c8bdd8b14a3ac576943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fc3cb687d9d078378225ac8afb8d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2140897e37d90c061140af7689598e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b97a949a7c7ac1cbeabee638299eb62.png)
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2 . 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 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)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)(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)
3 . 已知等差数列
中,第2项为6,前5项和为45.
(1)求
通项公式;
(2)若
,求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14eedc2934191808096c1808ca29f21.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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20-21高三上·上海浦东新·期中
名校
解题方法
4 . 已知无穷等比数列
的各项的和为3,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
5 . 已知等比数列
的首项为2,公比为
,其前
项和记为
,若对任意的
,均有
恒成立,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d489364bd65c69672b560f55bb2aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06430886275f5ad62bcda62fce691e99.png)
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2020-12-03更新
|
420次组卷
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4卷引用:上海市进才中学2021届高三上学期期中数学试题
上海市进才中学2021届高三上学期期中数学试题北京市平谷区第五中学2020-2021学年高二下学期第一次月考数学试题(已下线)考向15 等比数列-备战2022年高考数学一轮复习考点微专题(上海专用)上海市第二中学2024届高三上学期期中数学试题
6 . 数列
中,数列前
项和为
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c6e0c2d16cda7e8b2b8c588adeb8ae.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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206f41005864da14a7c421695f29721d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
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名校
解题方法
7 . 已知数列
满足:
,
,记数列
的前
项和为
,若对所有满足条件的列数
,
的最大值为
,最小值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d06ad126eef8c33fdcd8a55107fe7d.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559c1f3a1960160a74d45629b3bd6974.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3cf6f2bbe20a404fea41a4d2b1c4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d06ad126eef8c33fdcd8a55107fe7d.png)
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2020-12-03更新
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923次组卷
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10卷引用:上海市上海师范大学附属中学2021届高三上学期期中数学试题
上海市上海师范大学附属中学2021届高三上学期期中数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高二上学期开学考试数学试题上海市南汇中学2022届高三下学期期中数学试题上海市嘉定区、长宁、金山区2019-2020学年高三上学期期末数学试题2020届上海市长宁嘉定金山高三一模数学试题2020届上海市嘉定区高三一模数学试题上海市曹杨二中2020-2021学年高二上学期期中数学试题(已下线)专题4.2 等差数列-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第二册)安徽省宣城市郎溪县2021届高考仿真模拟考试数学(理)试题(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)
8 . 已知数列
满足
对任何正整数n均有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d1e0596476420fb430678bbfdcee4c.png)
,设
,则数列
的前2020项之和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942ed174dfdafaf5f0a68cac579110f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59bdd812ec2067bbdf43c999da249568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d1e0596476420fb430678bbfdcee4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e557df2f9aeecbc164482608a4c7c88b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586573c2f2efb721046606904b823e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
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2020-11-29更新
|
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7卷引用:2020届上海市浦东新区高三二模数学试题
2020届上海市浦东新区高三二模数学试题江苏省无锡市锡山高级中学2020-2021学年高二上学期10月阶段性考试数学试题(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)(已下线)押第14题 数列小题-备战2021年高考数学(理)临考题号押题(全国卷2)(已下线)专题03 等比数列及前n项和(专题测试)-2020-2021学年高二数学重难点手册(数列篇,人教A版2019选择性必修第二册)(已下线)4.3.2 等比数列前n项和1课时(已下线)第08讲 等差、等比数列- 1
9 . 定义:对于一个项数为
的数列
,若存在
且
,使得数列
的前
项和与剩下项的和相等(若仅为1项,则和为该项本身),我们称该数列是“等和数列”例如:因为3=2+1,所以数列3,2,1是“等和数列”.请解答以下问题:
(1)数列
是“等和数列”,求实数
的值;
(2)设数列
通项公式为
,且共有
项,证明:
不是等和数列;
(3)项数为
的等差数列
的前
项和为
,求证:
是“等和数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdcd07be0a24101e784b628d46ec90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfae43a1ea1f5f3a031d224ac61a5f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2c6eaa1e1c1f4c85e35b46e30b7c70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b933d363f5b85a6b4110c9ef030c56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378397148dc9a98bb9109154a551ced5.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/f899bd706e363ec439acbd0bea356209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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10 . 已知函数
各项均不相等的数列
满足
.令
.给出下列三个命题:(1)存在不少于3项的数列
使得
;(2)若数列
的通项公式为
,则
对
恒成立;(3)若数列
是等差数列,则
对
恒成立,其中真命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e115dd0cb0c28b33cdc1a43e9be779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6044fe76e20b5da7861f3d9b3f3143e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec26010780db181e89a51f780743f6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d87a9b5258b1a5eaee3b71004a4838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8fcccbb1234ad67314c96f9856e240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1a21f360eab1fb27b8cc15db4c04a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6273df1952961f128bb340bc28e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2cc49cadf5bf94f8df8318fa7bd519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
A.(1)(2) | B.(1)(3) | C.(2)(3) | D.(1)(2)(3) |
您最近一年使用:0次
2020-11-15更新
|
1711次组卷
|
6卷引用:2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题
2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题(已下线)数学-6月大数据精选模拟卷04(上海卷)(满分冲刺篇)上海市南洋模范中学2021届高三上学期期中数学试题(已下线)考向03 函数及其性质-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)考向15 等比数列-备战2022年高考数学一轮复习考点微专题(上海专用)上海交通大学附属中学2021-2022学年高一下学期5月线上月考数学试题