名校
解题方法
1 . 已知数列
,
,满足.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d5cab27eabd53067c84de78b399584.png)
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)若数列
满足
,对一切
都成立,求数列
的通项公式.
![](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/06d5cab27eabd53067c84de78b399584.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9396fb0ce65e74cab581a155c3c3fc98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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2017-04-01更新
|
1331次组卷
|
2卷引用:吉林省辽源五中2017-2018学年高一下学期第一次月考数学(文)试题
名校
2 . 已知数列
中,
,
(Ⅰ)求
;
(Ⅱ)猜想
的表达式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925f52e9e8f9143a737f9d9edfc72325.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6fe44bc49b478979589face327799.png)
(Ⅱ)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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2017-08-17更新
|
1343次组卷
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8卷引用:吉林省长春市第一中学2018-2019学年高二下学期第一次月考数学(理)试题
吉林省长春市第一中学2018-2019学年高二下学期第一次月考数学(理)试题山东省潍坊市2016-2017学年高二下学期期末考试数学(理)试题山东省潍坊寿光市2016-2017学年高二下学期期末考试理数试题(已下线)专题6.6 数学归纳法(讲)- 浙江版《2020年高考一轮复习讲练测》山西省太原市第二十一中学2019-2020学年高二下学期期中数学(理)试题安徽省合肥168中学凌志班2019-2020学年高二(下)入学数学(理科)试题(已下线)考点65 数学归纳法(讲解)-2021年高考数学复习一轮复习笔记(已下线)专题7.6 数学归纳法(练)-2021年新高考数学一轮复习讲练测
名校
3 . 已知
,
,
,
,求证:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac49619543ace1f24754240fcf6cb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574b3c0cdd4e1c6f3c77d43dc7e0603f.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026a8139e4a47badf8ce7b7f5945c19d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6df5d0852a9a40b8d18c356d302435.png)
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2017-05-03更新
|
640次组卷
|
3卷引用:吉林省实验中学2016-2017学年高二下学期第二次月考(5月)数学(理)试题
4 . 在数列
中,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明数列
是等比数列,并求数列
的通项公式;
(2)设
,
,求数列
的前
项和.
![](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/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c548da8d22f8f7e63361f174e788250b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6631307e8ff61b215f447f2527c36e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9411680e7b0690b0f8c8c78915897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33579e8caf3abbe4b6f899ca0350810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851e207ba24c77cdd32c0764c0cc6580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
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2017-05-22更新
|
1964次组卷
|
3卷引用:山东省烟台市2017届高三适应性练习(二)数学(理)试题
10-11高一下·吉林长春·期中
解题方法
5 . 已知数列
的前
项和为
,且对于任意
,都有
是
与
的等差中项,
(1)求证:
;
(2)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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d637866200a82ea682bba7da5a9d9f6.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456acf42591409e1b7dc6fe08f4672e4.png)
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解题方法
6 . 已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533d0527539eeb0e475383d532228c4f.png)
(1)若数列
满足
,求证:
是等比数列;
(2)若数列
满足
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533d0527539eeb0e475383d532228c4f.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0267d117cde8ccec5cb7c7043e8f130e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626732e34cf714726e34502994520b5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbbd4ac56deb291fc4aa1c976743506.png)
您最近一年使用:0次
2017-03-12更新
|
1463次组卷
|
2卷引用:2017届吉林省长春市普通高中高三下学期第二次模拟考试数学(理)试卷
名校
7 . 已知数列
满足
,
,
,其中
.
(1)求证:数列
是等差数列,并求出数列
的通项公式;
(2)设
,求数列
的前n项和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cab14eade796cbef480ebc572ea2399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381576e698a46df8c497e6b5f8346ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf4ba0fa4ee3bcc28e2cc60a4d57a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c380ffc39ccad63b15e331040720e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314898d22aaac1e3df0d2e1993829d19.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8046e745e78601ffb2b7c276eb663e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b6eaa1cac42bedb3556255ae38d4e4.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/cb26cd1601fe7e76e1e2dc0b4909324a.png)
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2017-03-21更新
|
1696次组卷
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5卷引用:吉林省扶余市第一中学2017-2018学年高一下学期期末考试数学试题
8 . 在数列
中,设
,且
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60940bb0676c66a4e8cc033ddc5fc2fd.png)
,且
.
(1)设
,证明数列
为等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2a16f300269c09eceee54cbc4712f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60940bb0676c66a4e8cc033ddc5fc2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d307ec71820b6536453fbdb5069da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8182f57c43fd1d8fb13161224687c469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](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)
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2017-03-22更新
|
1231次组卷
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2卷引用:2017届吉林省长白山市高三第二次模拟考试数学(文)试卷
9 . △ABC的三个内角A、B、C成等差数列,
分别为三个内角A、B、C所对的边,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://img.xkw.com/dksih/QBM/2016/7/18/1572925490126848/1572925495508992/STEM/0f48f30f2a294044a57d87387dbe8003.png)
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13-14高一下·安徽蚌埠·期中
真题
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10 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c454bd8f7d2a0bf38503cef6e126076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525d951d32c9b42ef36c58e9c5e9aaef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c454bd8f7d2a0bf38503cef6e126076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525d951d32c9b42ef36c58e9c5e9aaef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f07209a79bf05e8b861e5077cd74ae.png)
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2016-12-03更新
|
2108次组卷
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9卷引用:2019届吉林省东北师范大学附属中学高三年级下学期理科数学大练习(四)
2019届吉林省东北师范大学附属中学高三年级下学期理科数学大练习(四)(已下线)2013-2014学年安徽蚌埠铁中高一下学期期中质量检测数学试卷2013年普通高等学校招生全国统一考试文科数学(江西卷)(已下线)2013-2014学年安徽省蚌埠铁中高一下学期期中检测数学试卷2015-2016学年山东省菏泽市高二上学期期中考试数学A卷【全国百强校】宁夏银川一中2019届高三第五次月考数学(文)试题2019届湖南省永州市祁阳县高三下学期第二次模拟考试文科数学试题湖南省永州市祁阳县第四中学2024届高三上学期第三次段考数学试题陕西省西安市雁塔区第二中学2023-2024学年高二上学期第二次阶段性测评数学试题