1 . 已知数列
满足
,
,
,
是数列
的前
项和.
(1)若数列
为等差数列.
(ⅰ)求数列的通项
;
(ⅱ)若数列
满足
,数列
满足
,试比较数列
前
项和
与
前
项和
的大小;
(2)若对任意
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c815636f7576224e083acc591c0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9820afa03321a26c78c9da42a6488765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eba496d4777ab1fc260705dcc27852c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79fb82760a6867d08c4ab547e4f713f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c815636f7576224e083acc591c0b8.png)
(ⅰ)求数列的通项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4048ce0a0bd4711f6c391e1bc2a323c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ceff85f3aef661dddec99516836312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fffa80522acb58684e080d5dd0849a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ceff85f3aef661dddec99516836312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69726bca10112fb049f0f1a9cb1d4a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2 . 正项数列
满足:
.
(1)求数列
的通项公式
;
(2)令
,求数列
的前
项和
.
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/c627d04923d44fd2a221f8fa1a28427a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/08154ffeab404dd4a421da923c1932f0.png)
(1)求数列
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/c627d04923d44fd2a221f8fa1a28427a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/94308fa17b034c30befc7b9eeddbd868.png)
(2)令
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/2c21ca8ebbf44953ae955333a9400f81.png)
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/c627d04923d44fd2a221f8fa1a28427a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/7a1a2e8236134432acceca2419860a12.png)
![](https://img.xkw.com/dksih/QBM/2014/1/2/1571453167919104/1571453173555200/STEM/f6a02171784844ccbf30033bd9713e96.png)
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2016-12-02更新
|
666次组卷
|
3卷引用:2015届黑龙江省绥化市重点中学高三下学期期初开学联考理科数学试卷
2015届黑龙江省绥化市重点中学高三下学期期初开学联考理科数学试卷(已下线)2014届黑龙江佳木斯市第一中学高三第三次调研理科数学试卷2014-2015学年吉林省延边二中高二上学期期末考试理科数学试卷
12-13高三·江苏无锡·开学考试
3 . 已知数列
中,
,前
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2329745d9b7ab75e7cfcf926d68a70d9.png)
(Ⅰ)求证:数列
是等差数列; (Ⅱ)求数列
的通项公式;
(Ⅲ)设数列
的前
项和为
,是否存在实数
,使得
对一切正整数
都成立?若存在,求
的最小值,若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2329745d9b7ab75e7cfcf926d68a70d9.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
(Ⅲ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ea456f763fa4906ef919092a4f811a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a217c43ec95470b9f3aa8e2e9e0dd1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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4 . 已知首项为
的等比数列
的前n项和为
, 且
成等差数列.
(Ⅰ) 求数列
的通项公式;
(Ⅱ) 证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263927ecdc5b57118aa3c2e4896d2bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca640a4b772758cdf239d6522ba69c5.png)
(Ⅰ) 求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
(Ⅱ) 证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f441be60b9c13b03e28f79969b9c76.png)
您最近一年使用:0次
2016-12-02更新
|
3964次组卷
|
8卷引用:河北省重点中学2021届高三下学期开学考试(新高考)数学试题
河北省重点中学2021届高三下学期开学考试(新高考)数学试题2013年全国普通高等学校招生统一考试文科数学(天津卷)(已下线)2018年12月27日 《每日一题》(理数)人教必修5+选修2-1(高二上期末复习)-等差、等比数列的综合应用【全国百强校】山东省枣庄市第八中学东校区2019届高三10月单元检测(月考)数学(理)试题(已下线)专题18 等差数列与等比数列-十年(2011-2020)高考真题数学分项(已下线)考点14 数列的综合运用-备战2022年高考数学(文)一轮复习考点微专题(已下线)考点21 等差数列及其前n项和-备战2022年高考数学(文)一轮复习考点帮广西贺州市钟山中学2021-2022学年高二上学期9月月考数学试题
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5 . 设A是由m×n个实数组成的m行n列的数表,满足:每个数的绝对值不大于1,且所有数的和为零,记s(m,n)为所有这样的数表构成的集合.
对于A∈S(m,n),记ri(A)为A的第ⅰ行各数之和(1≤ⅰ≤m),Cj(A)为A的第j列各数之和(1≤j≤n):
记K(A)为∣r1(A)∣,∣R2(A)∣,…,∣Rm(A)∣,∣C1(A)∣,∣C2(A)∣,…,∣Cn(A)∣中的最小值.
对如下数表A,求K(A)的值;
(2)设数表A∈S(2,3)形如
求K(A)的最大值;
(3)给定正整数t,对于所有的A∈S(2,2t+1),求K(A)的最大值.
对于A∈S(m,n),记ri(A)为A的第ⅰ行各数之和(1≤ⅰ≤m),Cj(A)为A的第j列各数之和(1≤j≤n):
记K(A)为∣r1(A)∣,∣R2(A)∣,…,∣Rm(A)∣,∣C1(A)∣,∣C2(A)∣,…,∣Cn(A)∣中的最小值.
对如下数表A,求K(A)的值;
1 | 1 | -0.8 |
0.1 | -0.3 | -1 |
(2)设数表A∈S(2,3)形如
1 | 1 | c |
a | b | -1 |
求K(A)的最大值;
(3)给定正整数t,对于所有的A∈S(2,2t+1),求K(A)的最大值.
您最近一年使用:0次
2016-12-01更新
|
2602次组卷
|
2卷引用:北京市一零一中学2022届高三下学期入学考试数学试卷题
真题
名校
6 . 某公司一下属企业从事某种高科技产品的生产.该企业第一年年初有资金2000万元,将其投入生产,到当年年底资金增长了50%.预计以后每年资金年增长率与第一年的相同.公司要求企业从第一年开始,每年年底上缴资金d万元,并将剩余资金全部投入下一年生产.设第n年年底企业上缴资金后的剩余资金为an万元.
(Ⅰ)用d表示a1,a2,并写出
与an的关系式;
(Ⅱ)若公司希望经过m(m≥3)年使企业的剩余资金为4000万元,试确定企业每年上缴资金d的值(用m表示).
(Ⅰ)用d表示a1,a2,并写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
(Ⅱ)若公司希望经过m(m≥3)年使企业的剩余资金为4000万元,试确定企业每年上缴资金d的值(用m表示).
您最近一年使用:0次
2016-12-01更新
|
1279次组卷
|
10卷引用:福建省龙岩第一中学2021-2022学年高二下学期开学考数学试题
福建省龙岩第一中学2021-2022学年高二下学期开学考数学试题2012年全国普通高等学校招生统一考试文科数学(湖南卷)(已下线)题型09 求数列通项-2020届秒杀高考数学题型之数列(已下线)专题18 等差数列与等比数列-十年(2011-2020)高考真题数学分项人教A版(2019) 选择性必修第二册 过关斩将 全书综合测评高中数学解题兵法 第六十一讲 递推法人教B版(2019) 选修第三册 一蹴而就 第五章 单元测试卷1.4数列在日常经济生活中的应用检测A卷(基础巩固)(已下线)1.4数列在日常经济生活中的应用(分层练习,7大考点)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)FHsx1225yl188
11-12高三下·江苏·开学考试
7 . 对于数列
,如果存在一个正整数
,使得对任意的
都有
成立,那么就把这样一类数列
称作周期为
的周期数列,
的最小值称作数列
的最小正周期,以下简称周期.例如当
时
是周期为1的周期数列,当
时
是周期为4的周期数列.
(1)设数列
满足
不同时为0),求证:数列
是周期为6的周期数列,并求数列
的前2012项的和
;
(2)设数列
的前
项和为
,且
.
①若
,试判断数列
是否为周期数列,并说明理由;
②若
,试判断数列
是否为周期数列,并说明理由;
(3)设数列
满足
数列
的前
项和为
,试问是否存在实数
,使对任意的
都有
成立,若存在,求出
的取值范围;不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323d114a36d56466c003ac4720df4279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126141b8d68abc6a0823fade2f1b8127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e678480d8af30c1a839e3a24dd86dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6098c4e099ea82ec1e0f2c19b19b9d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc077744a63dd358c65150dd772b549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfa0b9b7a076b0fe847ce0e236a6dfb.png)
(2)设数列
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1776c2e71b0b25d84156d526c8984c62.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38ac38efc5f58e833f21c725e9711c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bed10de064f0cf8185a91d8a5623222.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6638000ee0c0bb0090a5691626375587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
您最近一年使用:0次
11-12高三下·吉林长春·开学考试
8 . 在数列
中,
,
为常数,
,且
,
,
成公比不为1的等比数列.
(1)求
的值;
(2)设数列
的前
项和为
,试比较
与
的大小,并说明理由.
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/101d9029853b4eb5b4c428bbefb5f044.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/7244d261f22d464dbcfc05305b697c08.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/dc263f95fc9a40c18323419540759410.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/cc0b7edc6bdc42f096c4a0c1ab123ea0.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/b11bbc11b5b94752bfccb9889a7c159b.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/45a5f7aae855417cb27b5cce0eb670f8.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/1e64f717707247f2ad6b8565ac71f30c.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/c95ed8373ab94310add7cf1cc9d1516b.png)
(2)设数列
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/101d9029853b4eb5b4c428bbefb5f044.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/772a160bacff41db8dcf98c782603a3b.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/bbec8a413fdb45b19efb196acf8baef9.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/bbec8a413fdb45b19efb196acf8baef9.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777179717632/1570777185107968/STEM/d3028826ea9349d7bfeaad8d5b8bc3a5.png)
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11-12高三下·江苏淮安·开学考试
名校
9 . 设数列
的前n项和为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87b20eb44e3ae0524c079c2a98f58a1.png)
(1)求证:数列
是等比数列;
(2)若
,是否存在q的某些取值,使数列
中某一项能表示为另外三项之和?若能求出q的全部取值集合,若不能说明理由.
(3)若
,是否存在
,使数列
中,某一项可以表示为另外三项之和?若存在指出q的一个取值,若不存在,说明理由.
![](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/a87b20eb44e3ae0524c079c2a98f58a1.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21cfd1ad0f4254be1d88c6577b6bbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a1d64cfdcbe9c17e524b3db3ec74d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce88d420679efae6f47b9a3bd5b16b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2016-12-01更新
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931次组卷
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4卷引用:2012届江苏省淮阴中学高三下学期数学综合练习(1)
(已下线)2012届江苏省淮阴中学高三下学期数学综合练习(1)江苏省淮安市淮阴中学2019-2020学年高三下学期4月综合测试数学试题江苏省南通市如皋中学2020届高三(创新班)下学期6月高考模拟数学试题江苏省南京市金陵中学2020届高三下学期6月考前适应性训练数学试题
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10 . 已知数列
和
的通项公式分别为
,
(
),将集合
中的元素从小到大依次排列,构成数列
.
⑴ 求
;
⑵ 求证:在数列
中、但不在数列
中的项恰为
;
⑶ 求数列
的通项公式.
![](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/9a4ffa30ea4719cd420242ed7c13ff99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5c2257dc005f0199c78d759d715f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452582cf1b406f40f48025ea5ff16e91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a3b1b5c91d29668b3af2188e082047.png)
⑴ 求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9655c9c1023982601709678d2dd2c18a.png)
⑵ 求证:在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a16b29e4dafabe6ec13a78d0ffd40b7.png)
⑶ 求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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2016-11-30更新
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1130次组卷
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8卷引用:上海市南洋模范中学2022-2023学年高二上学期开学考试数学试题
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