名校
解题方法
1 . 已知数列
满足
,
,
,
.
(1)证明:数列
为等差数列,并求数列
的通项公式;
(2)若
,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/40f4e1236d7dc0366d9523d0cbb426be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b039543372ce127c7b85782a118f0f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452441c97433c6dee7d6a8dd4aaa7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21051c2cb82f0cf87d005dc258ec9847.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/c55e9df52276e2d89c646a0714bbee8f.png)
您最近一年使用:0次
2021-02-02更新
|
1516次组卷
|
7卷引用:【新东方】绍兴高中数学00034
(已下线)【新东方】绍兴高中数学00034(已下线)【新东方】绍兴高中数学00038浙江省嘉兴市2020-2021学年高三上学期期末数学试题江苏省苏州中学2020-2021学年高二下学期期初质量评估数学试题(已下线)专题24 数列(解答题)-2021年高考数学(理)二轮复习热点题型精选精练(已下线)专题22 数列(解答题)-2021年高考数学(文)二轮复习热点题型精选精练(已下线)专题23 数列(解答题)-2021年高考数学二轮复习热点题型精选精练(新高考地区专用)
2 . 已知
满足
,
.
(Ⅰ)证明
是等差数列;
(Ⅱ)求
的前
项和
;
(Ⅲ)若
,
的前
项和是
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43398c56012e0debe1362dec5598e84e.png)
(Ⅰ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
(Ⅱ)求
![](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)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86769468331da06dd7662aa6d986fc4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
3 . 设
为数列
的前
项和,已知
,
.
(1)求出
,
的值,并证明:数列
为等比数列;
(2)设
,数列
的前
项和为
,求证:
.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077fe52ca6a0cb41d46f4dbc965af1e5.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83cf578e283612cb8782f67cb5ee11d.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5319070a0e6ea62c4216c48d010dce3f.png)
您最近一年使用:0次
名校
解题方法
4 . 已知数列
中,
,其前
项的和为
,且当
时,满足
.
(1)求证:数列
是等差数列;
(2)证明:
.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c154da7ed535cfd1edf19bc6d907ae.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd74d291484f4da59ac2149d2ec135c.png)
您最近一年使用:0次
2019-12-01更新
|
1846次组卷
|
7卷引用: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
解题方法
5 . 设Sn为数列{an}的前n项和,已知a2=3,Sn=2Sn﹣1+n(n≥2)
(1)求出a1,a3的值,并证明:数列{an+1}为等比数列;
(2)设bn=log2(a3n+1),数列{
}的前n项和为Tn,求证:1≤18Tn<2.
(1)求出a1,a3的值,并证明:数列{an+1}为等比数列;
(2)设bn=log2(a3n+1),数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b8aeb9c72a1c1ce0e8ce2962f33386.png)
您最近一年使用:0次
名校
6 . 已知数列
满足
,其中
.
(1)设
,求证:数列
是等差数列,并求出数列
的通项公式;
(2)设
,数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b70f7ba6edb8cbd2b95f0e92883746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c380ffc39ccad63b15e331040720e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2448cf72af76b810310e4cfb9818e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c108f901a9f72dc1355fd0fd18ae5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68778f67c1cb5a44d18e6a3537f91e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb26cd1601fe7e76e1e2dc0b4909324a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dfef48dec60a9bf78d55569b41f5d3.png)
您最近一年使用:0次
名校
7 . 已知数列
中,
,其前
项的和为
,且满足
.
(1)求证:数列
是等差数列;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.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/de4a643e34e4fe80e2e44d73798bb50e.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83668ff336589f82a2cd04db9f9947.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141ea73b476066881212512ecd3bb8a1.png)
您最近一年使用:0次
名校
8 . 已知数列
中,
,
(
),
.
(1)证明:数列
为等差数列,并求出数列
通项公式;
(2)设
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f1e4ae0f73b3ca199ffd7b2c7af5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd2b2b1c9c82997b28888cef839e67b.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebdf7b1804ea9d1ad03f7a9a04f4f0d.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02e80983b88cdf6b540502816c87d13.png)
您最近一年使用:0次
名校
9 . 已知数列
前
项和为
,满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e375b8b3791ee98dab11cd97b6379f.png)
(1)证明:数列
是等差数列,并求
;
(2)设
,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/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e375b8b3791ee98dab11cd97b6379f.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f543f3aafa4740bd65aefc8d8de4b6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ac75838b14085b34c59a0eb385ac4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b340e6cfa6ab9b97da7409f2db62c00.png)
您最近一年使用:0次
2016-12-03更新
|
865次组卷
|
5卷引用:【全国百强校】黑龙江省哈尔滨市第六中学2018-2019学年高一下学期期中考试数学试题
名校
10 . 在单调递增数列
中,
,且
成等差数列,
成等比数列,
.
(1)①求证:数列
为等差数列;
②求数列
通项公式;
(2)设数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5786daa387797fe28543eb25cdcf0193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48aa8f272b068a13e9a61912ed5697cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee635f30f8c1ab7cc90ca44ea5071f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd2bfef3925d6f9f46b96b301c58223.png)
(1)①求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fffabc2dfb59ac198c06dbcadfa75c.png)
②求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a44cfbb86a4eb76261c00ddc6bff181.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/9fea6ba08b4985e51979378af23595d5.png)
您最近一年使用:0次
2016-12-04更新
|
970次组卷
|
4卷引用:2016-2017学年湖北省孝感市七校教学联盟高一下学期期中考试数学(理)试卷
2016-2017学年湖北省孝感市七校教学联盟高一下学期期中考试数学(理)试卷2017届河北衡水中学高三上学期第二次调研数学(理)试卷河北省保定市定州中学2021届高三上学期期中数学试题(已下线)黄金卷13-【赢在高考·黄金20卷】备战2021年高考数学(文)全真模拟卷(新课标Ⅱ卷)