1 . 已知各项均为正数的数列
满足:
,
,
.
(1)若
,求证:数列
为等比数列,并求
的通项公式;
(2)设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac8419cf6c0e1d70ea5f5a9eb6dad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ee34488211deb77a6b963cce2b7c17.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c69eb385b052c234ba51e72811ea613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959074325305062891acf06078afae87.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/2b69f65365b0845d14e64cad8f395f23.png)
您最近一年使用:0次
解题方法
2 . 已知数列
的前
项和为
,且数列
是首项为5,公差为
的等差数列.
(1)求
的通项公式;
(2)令
,求数列
的前
项和
,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/4c09815106a2134d1699906e44228061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a38f98a978894ab7b68b6fbb935a38d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.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/5a8372c12b195d536036de2b1789c20a.png)
您最近一年使用:0次
名校
解题方法
3 . 已知各项都是正数的数列
的前
项和为
,
,
.
(1)求数列
的通项公式.
(2)设数列
满足:
,
,数列
的前
项和
.求证:
.
![](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/a3676c51d6987107ebd4aadbffd82abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176b6b574ad2c11248c2d39d4deaf04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.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/9c3fec47d2dd2b8099d86c87b6e57de8.png)
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解题方法
4 . 设
.是数列
的前n项和,
,其中k是常数.
(1)求
及
的值;
(2)当k=2时,求证:
;
(3)设
,记
,求证:当
时,
.
![](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/fa1e99d36a92db324c53e4ce68394b96.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)当k=2时,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d29840b9887dee6218b9bf1f7a3386.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6412b76e9b7b5c7bc713a72e9d6e210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b54727dbbee119fd09d4d03fe72bc6.png)
您最近一年使用:0次
名校
解题方法
5 . 已知数列
的前n项和为
.
(1)求这个数列的通项公式;
(2)设
,证明:对
,数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4558d082c4423ceacf45a1c4c663ac.png)
(1)求这个数列的通项公式;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60784a71f5014a4b04a0d0822e7f7d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7dcb089affa0643809362613254dcc.png)
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2021-01-24更新
|
1262次组卷
|
2卷引用:甘肃省金昌市第一中学2020-2021学年高一下学期期中考试数学(理)试题
名校
解题方法
6 . 已知数列
的前
项和为
,且满足
.
(1)求证:数列
是等比数列;
(2)记
,求证:数列
的前
项和
.
![](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/c2c33f6d1c1f9d800e35464e50479041.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1413bc2c9162794f2dde9193684696e.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddee3489c3fb87fd9664a73e52b2f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c215db1d8f69757118ad405b78035628.png)
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2021-04-10更新
|
3253次组卷
|
8卷引用:四川省南充市白塔中学2020-2021学年高一下学期4月月考数学试题
四川省南充市白塔中学2020-2021学年高一下学期4月月考数学试题东北三省四城市联考暨沈阳市2021届高三质量监测(二)数学试题(已下线)专题2.3 数列-常规型-2021年高考数学解答题挑战满分专项训练(新高考地区专用)广东省汕头市金山中学2022届高三上学期期中数学试题宁夏银川三沙源上游学校2021-2022学年高二上学期期中考试数学(文)试题湖南省常德市第二中学2020-2021学年高二(332班)下学期期中数学试题(已下线)第43讲 数列的求和四川省绵阳市三台中学2024届高三一模数学(理)试题(一)
名校
解题方法
7 . 在数列
中,
,
.
(1)求证:数列
是等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db922e8719eb7f817a7489e09632acc7.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf3da897eb73b729f66bb0d700775c5.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2020-10-17更新
|
1034次组卷
|
28卷引用:【全国百强校】黑龙江省鹤岗市第一中学2017-2018学年高一下学期期中考试数学(文)试题
【全国百强校】黑龙江省鹤岗市第一中学2017-2018学年高一下学期期中考试数学(文)试题【全国百强校】黑龙江省实验中学2017-2018学年高一下学期期末考试数学(文)试题【全国百强校】黑龙江省实验中学2017-2018学年高一下学期期末考试数学(理)试题安徽省淮南市第一中学2018-2019学年高一年级第二学期创新班第四次段考数学试题安徽省合肥二中2018-2019学年高一下学期期末数学(藏班)试题安徽省亳州市利辛县阚疃金石中学2019-2020学年高一上学期第三次月考数学试题四川省泸州市泸县第二中学2019-2020学年高一下学期期中考试数学试题吉林省长春市农安县实验中学2019-2020学年高一下学期期末考试数学试题福建省泉州市2017届高三(5月)第二次质量检查数学(理)试题【全国市级联考】广西壮族自治区岑溪市2017-2018学年高二下学期期末考试数学(文)试题【全国百强校】贵州省遵义航天高级中学2019届高三第四次模拟考试数学(理)试题【全国百强校】贵州省遵义航天高级中学2019届高三第四次模拟考试数学(文)试题(已下线)2019年12月25日《每日一题》必修5+选修2-1理数-数列求和的常用方法2020届陕西省西安交大附中学南校区高三上学期期中数学(理)试题黑龙江省鹤岗市第一中学2019-2020学年高二上学期开学考试(8月)数学(理)试题辽宁省大连市普兰店区第三十八中学2018-2019高二下学期第二次考试数学(理)试卷四川省阆中中学2020届高三适应性考试(一)数学(理)试题辽宁省本溪高级中学2019-2020学年高二9月月考数学试题江西省九江市同文中学2019-2020学年度高二上学期期末考试数学文科试题吉林省长春市实验中学2020-2021学年高三第一学期期中文科数学试题湖南师范大学附属中学2020-2021学年高二下学期第一次大练习数学试题江西省赣州市会昌县第五中学2020-2021学年高二上学期第一次月考数学(理)试题(已下线)突破4.2.2 等差数列的前n项和重难点突破-【新教材优创】突破满分数学之2020-2021学年高二数学重难点突破(人教A版2019选择性必修第二册)黑龙江省八校2021-2022学年高三上学期期中联合考试数学(文)试题(已下线)专题22 第一篇 热点、难点突破(测试卷二)(测)(理科)第一篇 热点、难点突破篇-《2022年高考理科数学二轮复习讲练测》(全国课标版)广东省佛山市南海区九江中学2021-2022学年高二下学期第二次月考数学试题江苏省连云港市海头高级中学2022-2023学年高二上学期第三次月考数学试题1号卷·A10联盟2022届全国高考第一轮总复习试卷数学(文科)试题(十一)
名校
解题方法
8 . 已知数列
的前
项和为
,且
,
.
(1)求证:
为等比数列,并求数列
的通项公式;
(2)若
,求数列
的前
项和
.
![](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/c3ddd6d99ad32dd7fdb1797d8cf94786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7584dd4a4b500c9d0b6ba28c02f9a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da72309d2507e2f5e5ed88d8cc08963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2020-10-01更新
|
425次组卷
|
5卷引用:福建省莆田第一中学2019-2020学年高一下学期期中考试数学试题
福建省莆田第一中学2019-2020学年高一下学期期中考试数学试题福建省莆田一中2019-2020学年高一(下)期中数学试题四川省绵阳市南山中学2020-2021学年高三下学期开学考试数学(理)试题(已下线)第四章 数列单元测试(基础版)课时训练-【新教材优创】突破满分数学之2020-2021学年高二数学课时训练(人教A版2019选择性必修第二册) 四川省绵阳南山中学2020-2021学年高三下学期开学考试理科数学试题
解题方法
9 . 已知数列
满足
,
.
(
)证明:
为等差数列.
(
)记数列
的前
项和为
,证明:
.
![](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/92f730cb250154602c124a8a641f1f16.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099a64d86bd0b4602578d910322adc1b.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc71a2fd8c6b263feea5ff5d6a36121.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/72db2104da094fc784dc30da3944772e.png)
您最近一年使用:0次
2021-06-22更新
|
1118次组卷
|
2卷引用:四川省乐山市十校2020-2021学年高一下学期期中数学试题
名校
解题方法
10 . 已知数列{an}与{bn}满足:
,且{an}为正项等比数列,a1=2,b3=b2+4.
(1)求数列{an}与{bn}的通项公式;
(2)若数列{cn}满足
,Tn为数列{cn}的前n项和,证明:Tn<1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac589532d72d4a4548213bc7577e9a6f.png)
(1)求数列{an}与{bn}的通项公式;
(2)若数列{cn}满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fe5d5b8a769a85192af60c927f2d46.png)
您最近一年使用:0次