解题方法
1 . 规定:对于任意实数
,若存在数列
和实数
,使
,则称
可以表示成
进制形式,简记为:
;如:
,表示
是一个2进制形式的数,且
;
(1)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
,试将
表示成
进制的简记形式;
(2)若数列
满足
,
,
,
,
,求证:
;
(3)若常数
满足
且
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db02c520989da5adce55d84410a644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5827acadcb93523ae7fa25204ebcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49fb140af76ff062c908e96e9dab466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69946ed268a024eca1cf522acee6985a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0328bf462207065c2e0eaaba1002ef1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aebf62d230cbee1781de6c1d73a7ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7f1ce82982b8385d78e8e77c8f1e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb701fb5c95b3612e64712d836754860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6ef8ef7af86ebdca4f34a36989a63.png)
(3)若常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e12b644318c5c276a086a82982b8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e909ffa98363a211839d0b1338afbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137510e8bcf483cdb40a0592140a800a.png)
您最近一年使用:0次
2 . 已知数列
中,
,
,且其前n项和
满足
(其中
),令
;
(1)求数列
的通项公式;
(2)若
,求证:
,
;
(3)
,求同时满足下列条件的所有a的值;
①对任意的正整数n,都有
;
②对任意的
,均存在
,使得当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8b7e459d1769b13c79bca8890c959c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37a2adb69dc49bb586de6477a1e36aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96f4711de10bdb4f6724f0a706f7913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce642b73be99b3c1a8c5dd38ec58eb28.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0438dfd927db90d7f5fcfff89aebfc14.png)
①对任意的正整数n,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa33d6f116c61ab89224c1a9886861cd.png)
②对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763756bfe137b23b3e9bcd9564b7b9ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c55f3b870ec43e1c778b2acd532e718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591c10d6af25780ba5bfcd82f2cb366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33591caf3f8bec653e47cd9b644ae9c5.png)
您最近一年使用:0次
3 . 已知数列
,
为其前
项的和,满足
.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,数列
的前
项和为
,求证:当
,
时
;
(3)已知当
,且
时有
,其中
,求满足
的所有
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f0f28c4d7360934da7f876a2695b52.png)
(1)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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09b1397026ef8f4a2762b896e4ba2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15526f7c892333030073b85fc3baee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26e76b5b7ba14cb838a2412cab235bb.png)
(3)已知当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831608f09609c37f757f5bfcd01253f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb29441c2acd6cbc81fd061af1274f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608cda4002a7c87561a248866771dc82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb7ba544e366503789e094747e1ffcac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2020-02-07更新
|
576次组卷
|
2卷引用:2016届上海市闸北区高考二模(理科)数学试题
4 . 已知数列
的各项均为整数,其前n项和为
.规定:若数列
满足前r项依次成公差为1的等差数列,从第
项起往后依次成公比为2的等比数列,则称数列
为“r关联数列”.
(1)若数列
为“6关联数列”,求数列
的通项公式;
(2)在(1)的条件下,求出
,并证明:对任意
,
;
(3)若数列
为“6关联数列”,当
时,在
与
之间插入n个数,使这
个数组成一个公差为
的等差数列,求
,并探究在数列
中是否存在三项
,
,
其中m,k,p成等差数列)成等比数列?若存在,求出这样的三项;若不存在,说明理由.
![](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/d33edde9e3f172bedd584b9e116a5abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在(1)的条件下,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae522c6514329f02e5cb1da8fa8c95db.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831608f09609c37f757f5bfcd01253f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8598379ec01edc16c72c1d3fa3ce81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904e7018ec79c8b0efdcb3ba67cb7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2554efe1860dc6c769c34d8cfa6de3e4.png)
您最近一年使用:0次
2020-02-07更新
|
506次组卷
|
2卷引用:2016届上海市闵行区高三上学期期末质量调研(一模)(文)数学试题
5 . 一青蛙从点
开始依次水平向右和竖直向上跳动,其落点坐标依次是
,(如图,
的坐标以已知条件为准),
表示青蛙从点
到点
所经过的路程.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/220d0549-124f-4dc9-b590-7ce2b6b0a176.png?resizew=157)
(1)点
为抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
准线上一点,点
,
均在该抛物线上,并且直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
经过该抛物线的焦点,证明
;
(2)若点
要么落在
所表示的曲线上,要么落在
所表示的曲线上,并且
,试写出
(不需证明);
(3)若点
要么落在
所表示的曲线上,要么落在
所表示的曲线上,并且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f5d00375f8083ff14dcf3745e4268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801c40c4b1b8b4155ccf08fc8df59342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f5d00375f8083ff14dcf3745e4268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/220d0549-124f-4dc9-b590-7ce2b6b0a176.png?resizew=157)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f5d00375f8083ff14dcf3745e4268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75ed10db4b9747a4b6d865b774f6b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfbb8b3c14e9617655321cab31acebc.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5661e7739636a3ff1479ab6a807d19b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0379cdb1fbe207a32568a978947fa41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e53542ad942e269a580a4dc7cc6fef.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf11327fc262b1351099455f6b9eed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02fa322f632dcd72048918b616511ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d55d2201d4d9aa7846b17a249ac528b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de918291423d4f2126ac8cc7d4b9edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772e1830de8a5b2bede8f5614d93a1d2.png)
您最近一年使用:0次
6 . 已知数列
的通项公式为
,其中
,
、
.
(1)试写出一组
、
的值,使得数列
中的各项均为正数.
(2)若
,
,数列
满足
,且对任意的
(
),均有
,写出所有满足条件的
的值.
(3)若
,数列
满足
,其前
项和为
,且使
(
、
,
)的
和
有且仅有
组,
、
、…、
中有至少
个连续项的值相等,其它项的值均不相等,求
、
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194a0334236a8656a975bb586247ecc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf486b5959f97ea7a64008db299ec8ab.png)
(1)试写出一组
![](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/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaa992a449b828df0ff545e233b279b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8a1ee5eeb4dbc2363ce98a96c290fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980d51ba3340a31964fbec9e6f243ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f955e61b70463e9bb6758f1f863a1675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17653e0cf31c86cdedbce1a76f7a0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fc67b1450f3cbb6ef3949d986c0f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0538b03aba1cc22a29acc35c116a4a52.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/ce9aade874a448b90b9e89adb7cefcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1109ca176d2be47347f68a3de238abd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f2c7c9305b404f7363a376af101aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
您最近一年使用:0次
2020-02-03更新
|
439次组卷
|
2卷引用:2016届上海市黄浦区高考二模(文科)数学试题
7 . 若数列
满足
则称
为
数列.记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f72c4ad89e8209cee415d23d752291.png)
(1)若
为
数列,且
试写出
的所有可能值;
(2)若
为
数列,且
求
的最大值;
(3)对任意给定的正整数
是否存在
数列
使得
?若存在,写出满足条件的一个
数列
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ee76d64af3138d8ae3f513b91620a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03796805b6aa7df7a5185efe5e5d4da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f72c4ad89e8209cee415d23d752291.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19822c77dddb12c67d95389bb529817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5c5b0b0a1114834e1431930cd3b7f0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c186dcbbd15895cbb4fedb84a7dc56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83233db4f5b58414f11a5b84e3676666.png)
(3)对任意给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0cf3042cb9bd240c68835a1432b455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20b4165a35c8f75bcba69fd335e8927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c4973ad119ab0298848998dafaa89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次
2020-02-03更新
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352次组卷
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2卷引用:2016届上海市虹口区高三5月模拟(三模)(理)数学试题
8 . 已知
,
,…,
是由
(
)个整数
,
,…,
按任意次序排列而成的数列,数列
满足
(
),
,
,…,
是
,
,…,
按从大到小的顺序排列而成的数列,记
.
(1)证明:当
为正偶数时,不存在满足
(
)的数列
.
(2)写出
(
),并用含
的式子表示
.
(3)利用
,证明:
及
.(参考:
.)
![](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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6188466f235e4e1ea2e31f2ba7c66fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7304f4a3860fb2ce6535b51166d21446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af09cf76bddbebeb560b2fd6e14c94a5.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc631d51fcb8adfef863d79c7af51098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7304f4a3860fb2ce6535b51166d21446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7304f4a3860fb2ce6535b51166d21446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)利用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328f89fc3962d57a2c15f91a69945014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6d3b3cda38ccba8ce44630bec332e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7f6d39982c903373565f3207ddb05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a3d41cba73d1ed67352c82556b742b.png)
您最近一年使用:0次
2020-02-02更新
|
454次组卷
|
2卷引用:2016届上海市黄浦区高三上学期期末调研测试(理)数学试题
名校
9 . 如图,圆
与直线
相切于点
,与
正半轴交于点
,与直线
在第一象限的交点为
. 点
为圆
上任一点,且满足
,以
为坐标的动点
的轨迹记为曲线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/f242e29e-3555-4909-bb3d-132d5f42e779.png?resizew=211)
(1)求圆
的方程及曲线
的方程;
(2)若两条直线
和
分别交曲线
于点
和
,求四边形
面积的最大值,并求此时的
的值.
(3)已知曲线
的轨迹为椭圆,研究曲线
的对称性,并求椭圆
的焦点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6912940c64a0bdb698c9af82fd2b7600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2613017de2e76bf8dd10295de827ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2252c40c265da6174adf8c90b11dfe54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4e5bf2fc46de6d148602f505614c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/f242e29e-3555-4909-bb3d-132d5f42e779.png?resizew=211)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)若两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4a45e79f51c7b5a9428f4cf2ab5c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41391e94da14cb86ba53a35b3c09a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a270ec7e23fc0cc1d4b04bf1d22184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
您最近一年使用:0次
名校
10 . 如图,圆
与直线
相切于点
,与
正半轴交于点
,与直线
在第一象限的交点为
.点
为圆
上任一点,且满足
,以
为坐标的动点
的轨迹记为曲线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/1ddfd004-c352-48bf-a123-2ee693682921.png?resizew=196)
(1)求圆
的方程及曲线
的方程;
(2)若两条直线
和
分别交曲线
于点
和
,求四边形
面积的最大值,并求此时的
的值.
(3)根据曲线
的方程,研究曲线
的对称性,并证明曲线
为椭圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6912940c64a0bdb698c9af82fd2b7600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2613017de2e76bf8dd10295de827ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2252c40c265da6174adf8c90b11dfe54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4e5bf2fc46de6d148602f505614c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/1ddfd004-c352-48bf-a123-2ee693682921.png?resizew=196)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)若两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4a45e79f51c7b5a9428f4cf2ab5c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41391e94da14cb86ba53a35b3c09a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a270ec7e23fc0cc1d4b04bf1d22184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)根据曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
您最近一年使用:0次