1 . 已知数列
中
,
,
.
(1)证明数列
是等比数列,并求
的通项公式;
(2)记
,
是数列
的前n项和,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705c826f3b3e084d2fdfcdbac7d18ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17d72d1d20d385920c3d9da6bed8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0530a06e7167d07eaf988f4c29f65f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4358c212e1f7ec327d2b738da67f0135.png)
您最近一年使用:0次
2022-04-08更新
|
639次组卷
|
3卷引用:河北省沧州市任丘市第一中学2023届高三上学期期中数学试题
名校
2 . 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:2017届河北衡水中学高三上学期第二次调研数学(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(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)
名校
解题方法
3 . 如图,在
中,D,E是边BC上的两点,
,AE平分∠BAC,
.
,求
的值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9680bd6f250acb8b568510419b59d3e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2332464d4d89c0ec731a79b98c01b043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970496276d831126182e9403a4f547eb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e276a2758f7a4175d4c4949b1fbb26.png)
您最近一年使用:0次
2024-04-30更新
|
269次组卷
|
2卷引用:河北省沧州市运东四校2023-2024学年高一下学期4月期中考试数学试题
名校
解题方法
4 . 已知数列
的前
项和为
,
,
,且
.
(1)证明:数列
是等差数列.
(2)求
的通项公式.
(3)若
,数列
的前
项和为
,证明:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0a39d93f6b19cbfcfe7a33d7a3ea7c.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832fd7a51831135b6ee6a01981db250e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936132b0b4c609369ee57e1908fe9c1a.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/83d76c3eb0a07a827877d7a4dc306211.png)
您最近一年使用:0次
2024-05-08更新
|
1444次组卷
|
3卷引用:河北省石家庄十五中2023-2024学年高二下学期期中数学试题
名校
解题方法
5 . 在数列
中,
,都有
成立.
(1)证明:数列
是等差数列;
(2)若数列
是首项为1的等差数列,求实数
的值及数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2409107e98dbd38ddae5bbe934f1bd2e.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
真题
名校
6 . 已知
是等差数列,
.
(1)求
的通项公式和
.
(2)设
是等比数列,且对任意的
,当
时,则
,
(Ⅰ)当
时,求证:
;
(Ⅱ)求
的通项公式及前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35e133418e9dbd8f81528b4b7ff9c25.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e8e5b901d8f8a8b6ec7740f1b55ed4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6bc55d5eb2c3d085b62ffcd8d138d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2daddb01510526b8fa639b18635e986d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e7d5ea07ebd45f587cbab2b3fd77ba.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99380bd8acd91cb1ffbd49e896d34f1d.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2023-06-08更新
|
12432次组卷
|
21卷引用:河北省邢台市邢台部分高中2024届高三上学期11月期中数学试题
河北省邢台市邢台部分高中2024届高三上学期11月期中数学试题2023年天津高考数学真题(已下线)专题7 等比数列的性质 微点2 等比数列前n项和的性质专题05数列(成品)(已下线)专题15 数列不等式的证明 微点1 反证法证明数列不等式(已下线)专题11 数列前n项和的求法 微点1 公式法求和(已下线)2023年天津高考数学真题变式题16-20江苏省淮阴中学等四校2023-2024学年高三上学期期初联考数学试题(已下线)第05讲 数列求和(练习)宁夏银川市第二中学2023-2024学年高二上学期月考二数学试卷(已下线)等差数列与等比数列(已下线)第3讲:数列中的不等问题【练】(已下线)重难点03:数列近3年高考真题赏析-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)专题6.2 等比数列及其前n项和【十大题型】(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)专题30 等比数列通项与前n项和(已下线)专题21 数列解答题(文科)-3(已下线)专题21 数列解答题(理科)-3安徽省六安第一中学2024届高三适应性考试数学试题专题06数列专题11数列
7 . 已知数列
的各项均为正数且均不相等,记
为
的前
项和,从下面①②③中选取两个作为条件,证明另外一个成立.
①数列
是等比数列;②
;③
是等比数列.
注:若选择不同的组合分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](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)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ced72f99d3e93cec09c40f24089b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9d317eec143a57c2511b0fb0767d43.png)
注:若选择不同的组合分别解答,则按第一个解答计分.
您最近一年使用:0次
2023-07-24更新
|
256次组卷
|
3卷引用:河北省石家庄市部分学校2023届高三下学期期中数学试题
名校
解题方法
8 . 已知
.
(1)若
.求证:
;
(2)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b40b1544e62be8b9e9f4dc9f2c0c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ff91f5b820c97913da435a082b7dc7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b155b33772898966d74d5eb0084df56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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2022-12-21更新
|
837次组卷
|
3卷引用:河北省曲阳县第一高级中学2023-2024学年高一上学期期中数学试题
解题方法
9 . 在
中,内角A,B,C所对的边分别为a,b,c,且满足
.
(1)证明:
.
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56735696c9d7c8052c0b6a2922ae8ed.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2264c134952d41fb9bcb90e6c72c83.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ec4e7815c0e96282e553a00d038b99.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,某景区绿化规划中,有一块等腰直角三角形空地
,
,
,
为
上一点,满足
.现欲在边界
,
(不包括端点)上分别选取
,
两点,并在四边形
区域内种植花卉,且
,设
.
(1)证明:
;
(2)
为何值时,花卉种植的面积占整个空地面积的一半?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354c20e085fe1a99a8be03bd1d16b2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ef1f4982526c6e714fa8c50fbf7e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a3d7e3d361117f56c3f02c82687f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a0982460d2fdf7f28aabe7f8ae01e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d8f7b924d985f3c4af8cb913271ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58605d04f34a2887781b049ca8f7c2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/22/2ad8ac62-f98a-45df-a499-c17b02ba1dfe.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14091f3f56eb41a8be016478e932bed8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2023-06-18更新
|
364次组卷
|
3卷引用:河北省唐山市十县一中联盟2022-2023学年高一下学期期中数学试题