名校
1 . 已知数列
的首项
,
是数列
的前
项和,且满足
.
(1)求数列
的通项公式;
(2)设数列
满足
,记数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/b384422e49fda99346512614aeb38429.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/3819480e1e624208f729ad8653e4f24f.png)
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2018-03-14更新
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4卷引用:甘肃省天水市第一中学2020-2021学年高二下学期开学考试数学(理)试题
名校
2 . 各项均为正数的等比数列
中,
.
(1)求数列
通项公式;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc94f38316d47706ef065231133f3f4a.png)
(1)求数列
![](https://img.xkw.com/dksih/QBM/2017/9/13/1773181606322176/1774631980072960/STEM/9623f70d5c1e41799b08560c0ccc9b81.png?resizew=31)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16e5ca46c1a15ab2782a7dea8ac3616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
您最近一年使用:0次
名校
3 . 若数列
的前
项和
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede5bb0c3f3972140cd1d4d7832a62f3.png)
(1)求证:数列是等比数列;
(2)设,求数列
的前
项和
.
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2017-10-09更新
|
5005次组卷
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13卷引用:甘肃省武威市第六中学2018届高三上学期第二次阶段性过关考试数学(文)试题
甘肃省武威市第六中学2018届高三上学期第二次阶段性过关考试数学(文)试题四川省成都市九校2017届高三下学期期中联考数学(文)试题重庆市第一中学2018届高三上学期期中考试数学(文)试题河北省承德市实验中学2018届高三上学期期中考试数学(理)试题2020年普通高等学校招生全国统一考试理科数学样卷(十二)云南省弥勒市第一中学2019-2020学年高二下学期第四次月考数学(理)试题(已下线)专题20 数列综合-2020年高考数学母题题源全揭秘(浙江专版)人教B版(2019) 选修第三册 必杀技 第五章 专题2 数列求和广东省佛山市顺德区容山中学2021-2022学年高二下学期期中数学试题云南省大理下关第一中学教育集团2022~2023学年高二上学期段考(二)数学(B卷)试题河北省高碑店市崇德实验中学2023届高三下学期3月月考数学试题宁夏石嘴山市平罗中学2022-2023学年高二下学期期中考试数学(理)试题云南省沧源佤族自治县民族中学2021~2022学年高二上学期期末考试数学试题
4 . 设数列
满足
,且
.
(1)求
,
,
的值.
(2)证明:数列
为等比数列,并求出数列
的前
项和
.
(3)若数列
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892283cce7545c241c7d536e4c03db04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb23f1b6940b40353ca3d6397d5c21e.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/08eb71ecf8d733b6932f4680874dbbf3.png)
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2017-11-03更新
|
973次组卷
|
2卷引用:甘肃省天水市第一中学2018届高三上学期第三阶段考试数学试题
10-11高三·甘肃天水·阶段练习
5 . 已知点
(n∈N*)都在直线
:
上,
为直线
与x轴的交点,数列{
}成等差数列,公差为1.
(Ⅰ)求数列{
},{
}的通项公式;
(Ⅱ)求证:
(n≥2,n∈N*).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55f0047ef12a2be5367fdd83b563340c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae342dcb93e0e6f017093cacc5ac977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(Ⅰ)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc88fc4153959ace70437087d3714190.png)
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名校
解题方法
6 . 函数
,数列
满足
.
(1)求证:数列
是等差数列;
(2)令
,若
对一切
成立,求最小正整数m.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d2856a8aab0a412d4b0b5340616499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682a01a2f96321048e807baf7fd64985.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b78e4a03d4595f14be42054b61dfc6.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1b51d6d3798a64eff83628627a2291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bae39eace05922121489e182566105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
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2016-12-03更新
|
815次组卷
|
3卷引用:2015-2016学年甘肃省嘉峪关市一中高二上学期期中考试理科数学试卷
11-12高三上·广东·阶段练习
7 . 已知数列
为等差数列,且
,
.
(1) 求数列
的通项公式; (2) 令
,求证:数列
是等比数列.
(3)令
,求数列
的前
项和
.
![](https://img.xkw.com/dksih/QBM/2013/2/22/1571120867049472/1571120872587264/STEM/5beaf513ad544281adddd789bfe36dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8713c0a55c04fe0fc20259095d63c631.png)
(1) 求数列
![](https://img.xkw.com/dksih/QBM/2013/2/22/1571120867049472/1571120872587264/STEM/5beaf513ad544281adddd789bfe36dec.png)
![](https://img.xkw.com/dksih/QBM/2013/2/22/1571120867049472/1571120872587264/STEM/13b56fcc1c894a0bb8aaee35ab8b4f2c.png)
![](https://img.xkw.com/dksih/QBM/2013/2/22/1571120867049472/1571120872587264/STEM/603eca813dc040ce81c33e4de8c2af4c.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca857b7a6a1fe09827ecaa5f4c036069.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/08eb71ecf8d733b6932f4680874dbbf3.png)
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2016-12-01更新
|
866次组卷
|
4卷引用:甘肃省兰州四中2018-2019学年高二上学期期中考试数学试题
甘肃省兰州四中2018-2019学年高二上学期期中考试数学试题(已下线)2012届广东省培正中学高三11月月考文科数学(已下线)2012-2013学年广东省执信中学高一上学期期末考试数学试卷云南省玉龙纳西族自治县田家炳民族中学2019-2020学年高一下学期第一次月考数学试题
8 . 已知函数
对任意实数p、q都满足
,
.
(Ⅰ)当
时,求
的表达式;
(Ⅱ)设
求
;
(Ⅲ)设
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddb97b4b7f39bd68cba6be8f0a05086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d07dae3e9720f6a35cd3562b10fbef8.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee99a979f0ef8a84d9c44046af42fe96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fba55c498b0831d4128f8938af2941.png)
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640319e93c8bea1e03e466ec2785f368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8b0cf4e5dd8a0890b869f6167ac3ee.png)
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2011·山东济南·高考模拟
解题方法
9 . 在数列
中,
,并且对于任意
,都有
.
(1)证明数列
为等差数列,并求
的通项公式;
(2)设数列
的前
项和为
,求使得
的最小正整数
.
![](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/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950c6303c2ec03e48137be8addf9245c.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7706e0dba93c9f25c28bc8b01de44b70.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/fb3b52b4c0b54401a1dfc035c43edd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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