名校
1 . 弓琴,是弓琴弹拨弦鸣乐器(如下左图).历史悠久,形制原始,它脱胎于古代的猎弓,也可以称作“乐弓”,是我国弹弦乐器的始祖.古代有“后羿射十日”的神话,说明上古生民对善射者的尊崇,乐弓自然是弓箭发明的延伸.古代传说将“琴”的创始归于伏羲,也正由于他是以渔猎为生的部落氏族首领.在我国古籍《吴越春秋》中,曾记载着:“断竹、续竹,飞土逐肉”. 常用于民歌或舞蹈伴奏.流行于台湾原住民中的布农、邹等民族聚居地区.弓琴的琴身下部分可近似的看作是半椭球的琴腔, 其正视图即为一椭圆面,它有多条弦, 拨动琴弦,发音柔弱,音色比较动听,现有某专业乐器研究人员对它做出改进,安装了七根弦,发现声音强劲悦耳.如下右图,是一弓琴琴腔下部分的正视图.若按对称建立如图所示坐标系,
恰为左焦点,
均匀对称分布在上半个椭圆弧上(
在
上的投影把线段
八等分),
为琴弦,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25f54545acd154c90bb0f06c2e9c439.png)
,数列
前n项和为
,椭圆方程为
,且
,则
的最小值为_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb7709c7788a7cc03e0b54bd13d8756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9f9382c8d6a8bbaf25e2ea0e5a80b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7196c2669444cf50ca0b724093009dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25f54545acd154c90bb0f06c2e9c439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a2ebe3f11ddc1508b8d9063d244650.png)
![](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/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb6b91aca117fb3852d3d7ae5c81838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec49e42b284ccf0a4cf0de7a17aba3c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/99c26e15-35a6-4fdc-9f5b-84ba7e36ce1a.png?resizew=328)
您最近一年使用:0次
2022-11-23更新
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465次组卷
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2卷引用:湖南省郴州市原创试题评比参评2022届高三高考模拟数学试题(安仁一中命制)
2 . 已知公比为
的无穷等比数列
各项的和为9,无穷等比数列
各项的和为
.
(1)求数列
的首项
和公比q;
(2)对给定的
,设
是首项为
,公差为
的等差数列,求
的前10项之和;
(3)设
为数列
的第i项,
,求
,并求正整数
,使得
存在且不等于零.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9f0aaaa2695dff4b08d7a52e4c905e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34349ccffb9d86fe0f4d17e09b2e8922.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)对给定的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795da436610505275a05cdb45a1b7ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac24dd2ff15d115696e8a9f8dad264f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c66a0c50c32fba396a322f0ddbeda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3cb716b6e5aa5362937b4b4c860d48d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cebeb6ddcb38af59b6bffb3b5fd84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7dcca2acb8fb6e6a6933a02e0a130b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884ce1e9436d39f34f6d3116cb2a140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4723e6d9fb30562c1ff7fc723103469f.png)
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名校
解题方法
3 . 记
为等差数列
的前
项和,已知
,则( )
![](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/e71f5e79a50d0f2081b0fc33af6e9131.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-06-21更新
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478次组卷
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2卷引用:辽宁省名校联盟2021-2022学年高二下学期6月份联合考试数学试题
名校
4 . 已知数表如图,记第
行,第
列的数为
,如
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcdb51d05a2749e6bef432d3bbe6ce0.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2116faa9515a1042a00d7d976fa05dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8579684c249009bdadfedb56de56a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcdb51d05a2749e6bef432d3bbe6ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed92a4257671701925aaefdbfcaee03e.png)
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2022-05-14更新
|
299次组卷
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2卷引用:陕西省2022届高三下学期教学质量检测(三)理科数学试题
5 . 设数列
,若存在常数
,对任意小的正数
,总存在正整数
,当
时,
,则数列
为收敛数列.下列关于收敛数列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c29bfcb2e31e3c21967ede660eaa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921c6a888803a9e2ac2d7411e32ef834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.若等比数列![]() ![]() |
B.等差数列不可能是收敛数列 |
C.设公差不为0的等差数列![]() ![]() ![]() ![]() |
D.设数列![]() ![]() ![]() ![]() ![]() ![]() |
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2022-04-29更新
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583次组卷
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4卷引用:上海市徐汇区2022届高三三模数学试题
名校
解题方法
6 . 已知数列
的通项公式为
,记数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681967bfbdcdae96320e06da896b4da4.png)
__________ ,
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ed4b8cc130d1eab232d399d4066f5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91adba8efbf964e9e35547b0fd0ea36.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/681967bfbdcdae96320e06da896b4da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d200aac7c303cc885b22406e18ac90.png)
您最近一年使用:0次
2022-03-16更新
|
355次组卷
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3卷引用:河北省沧州市任丘第一中学2021-2022学年高二上学期期末数学试题
河北省沧州市任丘第一中学2021-2022学年高二上学期期末数学试题河北省沧州市2021-2022学年高二上学期期末数学试题(已下线)高二上学期期末【压轴60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
7 . 已知函数
.
(1)若
的反函数是
,解方程:
;
(2)当
时,定义
,设
,数列
的前n项和为
,求
、
、
、
和
;
(3)对于任意
、
、
,且
,当
、
、
能作为一个三角形的三边长时,
、
、
也总能作为某个三角形的三边长,试探究
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce427e97019745d570dd2728027fba5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8c44eaf91d997e5c18f0fba5729091.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fa6fcc95803182baf90fff837fb59c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9458d0ea1d42ff521691fe527c82519e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ba9740ba25181e1e03e2296671233d.png)
![](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/e72adb45c60c2f63b46e65ff787302bf.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5e69a1736fce183c0227c991c14810.png)
(3)对于任意
![](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/688b529596400ce9ab3fe9fbbd7f9408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4311879d4914afb91646bc4d816c29e3.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f484115a9df1b6060d6b14df85c6f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35770a47ffcba6bf1d94eceabb416d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee0882f5f575d9e0ae7677efbd41b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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解题方法
8 . 已知
是数列
的前n项和,若
,
,
,则下列结论正确的是( )
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b705f6ee1a9a9df0a3f8e9c17d6c5f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31804e942c396c2d262c6cf29ab7054e.png)
A.![]() | B.数列![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-02-21更新
|
885次组卷
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7卷引用:福建省漳州市2021-2022学年高二上学期期末质量检测数学试题
福建省漳州市2021-2022学年高二上学期期末质量检测数学试题黑龙江省哈尔滨市第六中学校2021-2022学年高二下学期期中考试数学试题(已下线)高二数学下学期期末精选50题(压轴版)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)福建省龙岩第一中学2022-2023学年高二(物理类实验班)上学期第一次月考数学试题福建省泉州市第九中学2022-2023学年高二上学期12月份月考数学试题第一章 数列(B卷·提升能力)(已下线)高二上学期期末【压轴60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
9 . 若数列
满足
的前
项和为
,下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8070352da3bc875fa0979fa5758aae57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-02-08更新
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559次组卷
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3卷引用:重庆市部分区2021-2022学年高二上学期期末联考数学试题
重庆市部分区2021-2022学年高二上学期期末联考数学试题(已下线)高二数学下学期期末精选50题(压轴版)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)重庆市江北区字水中学2023-2024学年高二上学期第四次月考数学试题
名校
解题方法
10 . 已知数列
满足
且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d691eee418a0db9d30f25bf3cec9880.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a01636bd1780785b082d04934f165e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a96fe92222542f2881eb5b82dfd11b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d691eee418a0db9d30f25bf3cec9880.png)
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2021-10-31更新
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544次组卷
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3卷引用:广西河池市八校2021-2022学年高二上学期第一次联考数学(理)试题