名校
解题方法
1 . 已知数列
的前n项和
,函数
对任意的
都有
,数列
满足
.
(1)分别求数列
、
的通项公式;
(2)若数列
满足
,
是数列
的前n项和,是否存在正实数
,使不等式
对于一切的
恒成立?若存在请指出
的取值范围,并证明;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/13e809fa3b46df42d384c2ba755b8902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2493344c3e6aa5e038c98ee6d60bb62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb6fef9df18b52be38a86b35953e485.png)
(1)分别求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07953530e3c248b3438fb200fb1661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4a4654967f312bfcc84872a000f767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-09-24更新
|
707次组卷
|
8卷引用:【全国市级联考】四川省眉山市高中2020届第二下期期末数学试卷
【全国市级联考】四川省眉山市高中2020届第二下期期末数学试卷(已下线)专题04数列求和的6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)四川省眉山第一中学2017-2018学年高一下学期期末考试数学试题广东省梅州市2018-2019学年高一下学期期末数学试题江西省新余市渝水区第一中学2019-2020学年高二上学期第一次月考数学(理)试题(已下线)第04周周练(拓展二:数列求和)福建省龙岩第一中学2022-2023学年高二(物理类实验班)上学期第一次月考数学试题广东省佛山市三水中学2019-2020学年高一下学期第二次统考数学试题
2 . 设
,
是函数
的图象上的任意两点.
(1)当
时,求
的值;
(2)设
,其中
,求
;
(3)对应(2)中
,已知
,其中
,设T为数列
的前n项和,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43aaf5088a5e0f2f3c85b1d39326d242.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8d8441014892f9ad3dbaad3f89774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc8f775c0c874c4ea920136a91db8f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208de3931b3ab66e2880a3bfe32d9afd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)对应(2)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7cf140605953920ee42014b6b99626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25673902449184f5727cbc786aa82a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ba74f65acbf50f8c3e7f97de19198d.png)
您最近一年使用:0次
2021-01-05更新
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4卷引用:江苏省常州市前黄高级中学2019-2020学年高二上学期期末数学试题
3 . 设数列
是公差为
的等差数列.
(1)推导
的前
项和
公式;
(2)证明数列
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(1)推导
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
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2016-12-04更新
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3卷引用:2015-2016学年内蒙古赤峰市宁城县高二上学期期末文科数学试卷
2015-2016学年内蒙古赤峰市宁城县高二上学期期末文科数学试卷2015-2016学年内蒙古赤峰市宁城县高二上学期期末考试文科数学试卷(已下线)第4.4讲 数列求和综合应用-2023-2024学年新高二数学同步精讲精练宝典(人教A版2019选修第二、三册)