1 . 在无穷等比数列
中,
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49496a272eddd4b431ecbfbb1f22409e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
2 . 已知定义域为
的函数
满足:①对
,恒有
;②当
时,
.
(1)求
的值;
(2)求出当
,
时的函数解析式;
(3)求出方程
在
中所有解的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe896777dc4f9aebb0e6b11ed3ed37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b8e9bb1e11d02cc2190a6e5ede4293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96c2c79f7d0a248ed590a0bce7eb8bd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166a53e132781c63d215c6c2cee3d306.png)
(2)求出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538190cf2a2e6f248188ae111a162ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf910f82c3094b267a3d481d23d829f.png)
(3)求出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf81798e77ead893922361d5e1d4548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5cf57d2484a1293cfd296a5ae2da1e.png)
您最近一年使用:0次
20-21高二下·上海浦东新·期中
3 . 正三棱锥
中,
,侧棱
长为2,点
是棱
的中点,定义集合
如下:点
是棱
上异于
的一点,使得
(
),我们约定:若
除以3的余数
,则
(例如:
、
等等)
(1)若
,求三棱锥
的体积;
(2)若
是一个只有两个元素的有限集,求
的范围;
(3)若
是一个无限集,求各线段
,
,
,…的长度之和(用
表示).(提示:无穷等比数列各项和公式为
(
))
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a099763f0877ec45ba3b45b0f346d342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e70a12f31060817b1e7bd42011ba11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f00adb86a0f84b29dc76d47d17732c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41d793c851a2f72f787913ba23e459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453c5f6d6b5d9f8d3ab84f8314bc3486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5d1a0de1c5bf6b550ff64da170afb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1532506d6a4f71dbe25d42181c924314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ac5f50f0ce9b75273fe7faa74bcb5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1b8bd8cc7643c27e27e5d31114a109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd665b428c47b29b1f4de1eb33105313.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e2c8d466ab8eb5ecd38060b53bbe8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f462c959206043521a129844bea5cce3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453c5f6d6b5d9f8d3ab84f8314bc3486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453c5f6d6b5d9f8d3ab84f8314bc3486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc2c634d91cf00c7ee4ae340a4026bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2451835b9ad821bc17a317bc0189a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881231f6c7cadb33580954af32fa1cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63f4bf7470364d01a625a927c144c9.png)
您最近一年使用:0次
4 . 已知
为等差数列
的前
项和,若
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e971d3adcb4d357d09b6788b118a41c.png)
(1)求数列
的通项公式;
(2)对于数列极限有如下常用结论:
,设
,用记号
表示
,试求
的值.
(3)从(2)的数列
中取出部分项按原来的前后顺序组成一个无穷等比数列
,且满足它的各项和等于
,试求出
的通项公式.
![](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/b1549723d901eeb2cf966e322f404a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e971d3adcb4d357d09b6788b118a41c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)对于数列极限有如下常用结论:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb948447262439c4f9484408cb5430c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ccd129274e6ff1acbf62d4283cb838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50532318393877acc90645a36548d168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f4a04c4ab5924fac3cb88310e972d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a339a8fb920efc3e1afc1244af6ec2d5.png)
(3)从(2)的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee5447f1268cfd1949810ba8db48308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
5 . 已知数列
满足
,且
,点
在二次函数
的图象上.
(1)试判断数列
是否为算术平方根递推数列?若是,请说明你的理由;
(2)记
,求证:数列
是等比数列,并求出通项公式
;
(3)在数列
中依据某种顺序从左至右取出其中的项
,…,把这些项重新组成一个新数列
,….若数列
是首项为
、公比为
的无穷等比数列,且数列
各项的和为
,求正整数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600ddda5beadd05fb0f12d628c96efe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23cd773ecfdd16ab5dfa2e1399001269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92cce4d6a70765a8342178894f6e2bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc78b2e900890d42a2caf610636415b4.png)
(1)试判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf2eb461d12fe388d51cc7f31bce02b.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7c067b1e4c594552b70ea764a749b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
(3)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c786d9fe63a1516cfe47cac846f39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f9e522d4ee0883959b69f348fd0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e43c7497cd191bca74dc396c9725a254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec6560ef6dc40fc680ef87bbd50001c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f4d1dfd429890baab33ca1a5a77d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3e9eb0c4bd9c899886668229c4c947.png)
您最近一年使用:0次
6 . 在平面直角坐标系中,函数
在第一象限内的图像如图所示,试做如下操作,把
轴上的区间
等分成
个小区间,在每一个小区间上作一个小矩形,使矩形的右端点落在函数
的图像上.若用
,表示第
个矩形的面积,
表示这
个矩形的面积总和.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/9d236159-b191-4908-8623-a647c6a3c36c.png?resizew=144)
(Ⅰ)求
的表达式;
(Ⅱ)请用数学归纳法证明等式:
;
(Ⅲ)求
的值,并说明
的几何意义.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff65953311c700ffe160fb0d8a1afc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff65953311c700ffe160fb0d8a1afc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5742a858aae33282f10a20f60a70498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/9d236159-b191-4908-8623-a647c6a3c36c.png?resizew=144)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
(Ⅱ)请用数学归纳法证明等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d890a201846c41fc9935565d0cce73.png)
(Ⅲ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58abe92020722722506c7b12c7879ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58abe92020722722506c7b12c7879ac5.png)
您最近一年使用:0次
2020-06-03更新
|
283次组卷
|
4卷引用:上海市青浦区2019-2020学年高二上学期期中数学试题
7 . 如图所示,已知
,
,对任何
,点
按照如下方式生成
,
,且
,
,
按逆时针排列,记点
的坐标为
(
),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f5ac0b0b8302aa86319c0bb83e1f8b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e24b666f44e97e5074a64942df8297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351feec5a48ca0f45897cd69407239e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c97d15ede1ffecd6035c4e196e557f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dabb54fef04a2a67ffe6e9795bfad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25840c9d3180843d35b1b5cd1b9eb6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039af66355ed85ff4c204931b882b694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c97d15ede1ffecd6035c4e196e557f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebadfbe0d52ea3bbdf6c7497460cb0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f5ac0b0b8302aa86319c0bb83e1f8b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/e4ea88b9-708c-4209-808a-d94f849dae08.png?resizew=273)
您最近一年使用:0次
名校
8 . 等差数列
的前
项和记为
,等比数列
的前
项和记为
,已知
,
为9,
,
.
(1)求数列
的通项
;
(2)设
,求
的最大值及此时的
的值;
(3)判别方程
是否有解,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.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/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/f7dcab692f76a2065309708160c673f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c8274fc6585b76e359a735bab1ade1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d898087ca0610ecb3ebaa4f5eb059d0d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36610b3aba63da0e46f6d008909c35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)判别方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a3c48b217e5aadcb6bf9935eb34ae.png)
您最近一年使用:0次
名校
9 . 平面直角坐标系中,已知点
.且
,当
时,点
无限趋近于点
,则点
的坐标是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2c1925576e98193778e5b7c5c100e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96aa8eee8bb725b27e3fcb14560e782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d154b00d2363a51a93657d941f07ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
10 . (1)若对任意的
,总有
成立,求常数
的值;
(2)在数列
中,
,求通项
;
(3)在(2)的条件下,设
,从数列
中依次取出第
项,第
项,
第
项,按原来的顺序组成新数列
,其中
试问是否存在正整数
,使得
且
成立?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c492077eb688232d237e14f843a580b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(2)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda873628018e3203981a03f91ef0dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8d1b6b0407652a0eb28d268004937d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734be5f414cfa40e8ed1d0f4083a2d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbbf4d763f3cbe5a71707bc19c78191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00c7ca6c76a50533e94da49d82576a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d676582bf28b1096c6ec7cea3e08b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831e34b763b383170381e6bbcd9e62f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fae014905a2ed7d363aa8ca839485aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d676582bf28b1096c6ec7cea3e08b2.png)
您最近一年使用:0次
2020-01-11更新
|
256次组卷
|
3卷引用:上海市外国语大学附属外国语学校2020-2021学年高二上学期12月月考数学试题
上海市外国语大学附属外国语学校2020-2021学年高二上学期12月月考数学试题(已下线)4.2无穷等比数列各项和(第3课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020选择性必修第一册)上海市南洋模范中学2015-2016学年高一下学期期末数学试题