1 . 已知正项数列
的前项积为
,且满足
.
(1)求证:数列
为等比数列;
(2)若
,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455e3d1c1bfb0b326c0e320f98e66b4c.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e7f1421d306e84f98d00b7c8652647.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198f065fed9980714262cc8aae060bb5.png)
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2021-12-12更新
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2557次组卷
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7卷引用:江苏省无锡市2021-2022学年高三上学期期中数学试题
江苏省无锡市2021-2022学年高三上学期期中数学试题江苏省南京市田家炳高级中学2021-2022学年高三上学期期中数学试题(已下线)重难点01 数列-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)高二数学下学期期中精选50题(压轴版)2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)专题26 数列的通项公式-4(已下线)专题10 数列通项公式的求法 微点5 构造法安徽省合肥市龙翔高复学校2023-2024学年高三上学期9月月考数学试题
19-20高三上·上海浦东新·期中
名校
解题方法
2 . 已知定义在
上的函数
和数列
满足下列条件:
,当
且
时,
且
,其中
均为非零常数.
(1)数列
是等差数列,求
的值;
(2)令
,若
,求数列
的通项公式;
(3)证明:
数列是等比数列的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52f8b9a9b16a01718a7e32244967966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13ee40e6cfa757f60396a5a93202c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25598fabdfa6d42d9a0005d93c5c662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1154f6a25bf87c6a1096794395dff17.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada7ecff631089128d70bb264b73df9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34dbe1cbc9299a7d10f69a1caf290933.png)
您最近一年使用:0次
2020-02-29更新
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527次组卷
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3卷引用:江苏省泰州市姜堰中学2020-2021学年高二上学期阶段测试一数学试题
江苏省泰州市姜堰中学2020-2021学年高二上学期阶段测试一数学试题(已下线)上海市华东师范大学第二附属中学2020届高三上学期期中数学试题2020届湖北省华中科技大学第二附中高三上学期期中数学试题
名校
3 . 已知数列
的前
项和为
,
且满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9934de714a873b75183d39b571a41a3.png)
(1)证明:
是等比数列,并求数列
的通项公式.
(2)设
,若数列
是等差数列,求实数
的值;
(3)在(2)的条件下,设
记数列
的前
项和为
,若对任意的
存在实数
,使得
,求实数
的最大值.
![](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/5786daa387797fe28543eb25cdcf0193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9934de714a873b75183d39b571a41a3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6dcabe57824f207cd826f947b32987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1946b2904d43e59b5a78a13947bceff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.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/b9b22c9d97c11e5a1adddb7665c6fcdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6babe165b30603457e1477a46ac2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2019-10-23更新
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942次组卷
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3卷引用:江苏省“百校大联考”2019-2020学年高三上学期第一次考试数学试题
名校
4 . 【江苏省南京师大附中2018届高三高考考前模拟考试数学试题】已知等差数列{an}和等比数列{bn}均不是常数列,若a1=b1=1,且a1,2a2,4a4成等比数列, 4b2,2b3,b4成等差数列.
(1)求{an}和{bn}的通项公式;
(2)设m,n是正整数,若存在正整数i,j,k(i<j<k),使得ambj,amanbi,anbk成等差数列,求m+n的最小值;
(3)令cn=
,记{cn}的前n项和为Tn,{
}的前n项和为An.若数列{pn}满足p1=c1,且对n≥2, n∈N*,都有pn=
+Ancn,设{pn}的前n项和为Sn,求证:Sn<4+4lnn.
(1)求{an}和{bn}的通项公式;
(2)设m,n是正整数,若存在正整数i,j,k(i<j<k),使得ambj,amanbi,anbk成等差数列,求m+n的最小值;
(3)令cn=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb8f04838c1533dc2aad1242a9257e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a6c58cee2ea71527427366047c3c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4753d52f2922bb12e91dac3c5bc105be.png)
您最近一年使用:0次
名校
5 . 已知数列
满足
,
,其中
,
,
为非零常数.
(1)若
,
,求证:
为等比数列,并求数列
的通项公式;
(2)若数列
是公差不等于零的等差数列.
①求实数
,
的值;
②数列
的前
项和
构成数列
,从
中取不同的四项按从小到大排列组成四项子数列.试问:是否存在首项为
的四项子数列,使得该子数列中的所有项之和恰好为2017?若存在,求出所有满足条件的四项子数列;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03f5a14384539bd77cfcab00c96fdeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3d2b68b6f7b9fdcbee1ada739cfbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1413bc2c9162794f2dde9193684696e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
②数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519af3f19dde038fab2e68b5e2a5387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519af3f19dde038fab2e68b5e2a5387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
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3卷引用:江苏省苏锡常镇四市2017届高三教学情况调研(二) (5月) 数学试题
江苏省苏锡常镇四市2017届高三教学情况调研(二) (5月) 数学试题江苏省盐城中学2018届高三上学期期末考试数学试题2(已下线)《2018届优等生百日闯关系列》【江苏版】专题二 第五关 以子数列或生成数列为背景的解答题