名校
解题方法
1 . 证明下列不等式:
(1)已知
,求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
,求证
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead56bb8f5e7a72e9f8640e795caf68d.png)
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2022-10-08更新
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2卷引用:湖南省株洲市九方中学2023-2024学年高一上学期9月月考数学试题B卷
2 . 在数列
中
,且满足
(
且
).
(1)证明:数列
为等比数列;
(2)求数列
的前
项和
.
![](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/1962ec26008093899dec76cbee62e5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d363b6982fee3bf1337d1542137a2f3d.png)
(2)求数列
![](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)
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2023-12-22更新
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5卷引用:湖南省长沙市宁乡市2024届高三上学期11月调研考试数学试题
湖南省长沙市宁乡市2024届高三上学期11月调研考试数学试题宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(四)江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(三)(已下线)考点4 等比数列的定义与判断 2024届高考数学考点总动员【练】(已下线)热点5-2 等比数列的通项及前n项和(6题型+满分技巧+限时检测)
3 . 在正项等比数列
中,
,
.
(1)求
的通项公式;
(2)若
,证明
是等差数列,并求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ae90518ab352bc6ac957287c05d819.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/08eb71ecf8d733b6932f4680874dbbf3.png)
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9卷引用:湖南省百校大联考2023-2024学年高二上学期12月联考数学试题
湖南省百校大联考2023-2024学年高二上学期12月联考数学试题河北省邢台市质检联盟2023-2024学年高二上学期第四次月考(12月)数学试题(已下线)高二数学上学期期末模拟试卷-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)重庆市九龙坡区八中科学城中学校2023-2024学年高二(艺术班)上学期期末数学试题重庆市第八中学校2023-2024学年高二艺术班上学期期末数学试题广东省汕头市金山中学2023-2024学年高二上学期期末考试数学试题云南省大理白族自治州民族中学2023-2024学年高二下学期见面考试数学试题广东省茂名市信宜市华侨中学2023-2024学年高二上学期第二次段考(1月)数学试题广东省珠海市斗门区第一中学2023-2024学年高二下学期第一次月考数学试题
4 . 已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35052e91056dd484cb6d300e6d9abbe2.png)
(1)令
,求证:数列
为等比数列;
(2)求数列
的前
项和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35052e91056dd484cb6d300e6d9abbe2.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702eda75c107e69d452e489a77b94662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](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)
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2023-11-23更新
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4卷引用:湖南省邵阳市武冈市2023-2024学年高三上学期期中考试数学试题
湖南省邵阳市武冈市2023-2024学年高三上学期期中考试数学试题陕西省西安市西安交大附中2024届高三上学期第六次诊断考试数学(文)试题(已下线)模块一专题2《数列的通项公式与求和》单元检测篇B提升卷(高二人教B版)(已下线)模块一 专题3《数列的通项公式与求和》单元检测篇B提升卷(高二北师大版)
解题方法
5 . 一般认为,民用住宅的窗户面积必须小于地板面积,但窗户面积与地板面积的比应不小于
,而且这个比值越大,采光效果越好.
(1)若一所公寓窗户面积与地板面积的总和为
,则这所公寓的窗户面积至少为多少平方米?
(2)若同时增加相同的窗户面积和地板面积,公寓的采光效果是变好了还是变坏了?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28555fa2f3a09261cb4e0305d390145.png)
(1)若一所公寓窗户面积与地板面积的总和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbe9c57a41246996feb8fc48a18b77a.png)
(2)若同时增加相同的窗户面积和地板面积,公寓的采光效果是变好了还是变坏了?请证明你的结论.
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2卷引用:湖南省湘西州花垣县民族中学2023-2024学年高一上学期期中数学试题
6 . 已知数列
满足
,且有
.
(1)证明:数列
是等比数列;
(2)求数列
的前
项和
.
![](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/dc1f918b30455fd7220fbd16a8704db9.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac633587ba2da63197c35031722602db.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9ac6f52f934bf88afc2e78a5585269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2023-09-01更新
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6卷引用:湖南省永州市双牌县第二中学2024届高三上学期开学摸底联考数学试题
名校
解题方法
7 . (1)设
,
,
,
均为正数,
且
,证明:
;
(2)已知
,
且
,比较
和
的大小.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62948164bee4ec540287564f801269a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a565a183d366ea8c68d7a92053f3c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef0e9d305e0fc426a0425911e54ea21.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e2bd4da6f51c9a9b0ead06cfdf89d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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2023-10-13更新
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2卷引用:湖南省部分学校2023-2024学年高一上学期10月联考数学试题
名校
解题方法
8 . (1)已知
,求
的取值范围.
(2)设
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe37c8be48c29fd36f87528478ae8bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e349aab7489f098bcea13bd5bc99a936.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0d138cbf50b7da8c88214ca6d917d8.png)
您最近一年使用:0次
名校
解题方法
9 . 已知等差数列的公差
,其前
项和为
,若
,
,
成等比数列,且
.
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ba3491b99cfbbfa5df0433fe8480d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
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2023-07-25更新
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4卷引用:湖南省湘潭钢铁集团有限公司第一子弟中学2024届高三8月开学考试数学试题
名校
10 . (1)已知
,
,
分别为
三个内角
,
,
的对边.请用向量方法证明等式
;
(2)若三个正数
,
,
满足
,证明:以
,
,
为长度的三边可以构成三角形.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34369422d71dd95c61cdd1b8245d7b6c.png)
(2)若三个正数
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba9192c300ab7108a36178e61a2d9c3.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
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2023-07-15更新
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2卷引用:湖南省长沙市雅礼中学2022-2023学年高二下学期期末数学试题