1 . 对于函数
,分别在
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”
(1)设函数
,记
“切线-
轴数列”为
,记
为
的前n项和,求
.
(2)设函数
,记
“切线-
轴数列”为
,猜想
的通项公式并证明你的结论.
(3)设复数
均为不为0的实数,记
为
的共轭复数,设
,记
“切线-
轴数列”为
,求证:对于任意的不为0的实数
,总有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ed953d6e0bd80a5da66552c7bfbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d48fa9493a86f262569df235a82ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8292395dc894796602a60486e575a808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef5756fec38d1b4dc62358b45c3352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bcf306a6aa8554d1d7fc8317f4e946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5f303f666e164582da05968d9d8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6f044a9b06a7a769e613c977cbfb87.png)
您最近一年使用:0次
2024-01-01更新
|
446次组卷
|
7卷引用:上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题
上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题(已下线)模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)(已下线)模块二 专题1 与曲线的切线相关问题(已下线)模块二 专题3 与曲线的切线相关问题(人教B版)(已下线)模块二 专题4 与曲线的切线相关问题(高二北师大版)(已下线)模块一 专题1 《导数的概念、运算及其几何意义》B提升卷(苏教版)(已下线)模块二 专题1 与曲线的切线相关问题(苏教版高二)
2 . 在平面直角坐标系
中,P,Q是抛物线
上两点(异于点O),过点P且与C相切的直线l交x轴于点M,且直线
与l的斜率乘积为
.
(1)求证:直线
过定点,并求此定点D的坐标;
(2)过M作l的垂线交椭圆
于A,B两点,过D作l的平行线交直线
于H,记
的面积为S,
的面积为T.
①当
取最大值时,求点P的纵坐标;
②证明:存在定点G,使
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb9603390e28948abd2e3cd96e1720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)过M作l的垂线交椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895f5fcb1cebfc09dc14ab6efad03437.png)
②证明:存在定点G,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac90c4158636c076ef1d0d45df68be88.png)
您最近一年使用:0次
2023-05-08更新
|
942次组卷
|
5卷引用:高二上学期期中复习【第三章 圆锥曲线的方程】十二大题型归纳(拔尖篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)
(已下线)高二上学期期中复习【第三章 圆锥曲线的方程】十二大题型归纳(拔尖篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)通关练17 抛物线8考点精练(3)山东省烟台市2023届高考适应性练习(一)数学试题山东省枣庄市2023届高三三模数学试题湖南省株洲市第二中学2022届高三下学期第三次月考数学试题
解题方法
3 . (1)已知直线
与抛物线
交于
,
两点,直线l与x轴相交于点
,求证:
;
(2)试将第(1)题中的命题加以推广,使得第(1)题中的命题是推广后得到的特例,并证明推广后得到的命题正确.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbc3a148fea86d30909dee2022fb384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f021572c9349d56120b7094c34126623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278c3598da951b73b53dc4a3929e65f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9393d79bf424855cae6938d125b201f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a65a75e6ec85f8fc5a2758edfef95c.png)
(2)试将第(1)题中的命题加以推广,使得第(1)题中的命题是推广后得到的特例,并证明推广后得到的命题正确.
您最近一年使用:0次
4 . (1)求证:
;
(2)求证:
;
(3)若m、n、r均为正整数,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588855663a97d8fc98e41368c9f0c887.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724a6dd2bb85b676a9ddbcb4d8ede156.png)
(3)若m、n、r均为正整数,试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ca3166112603878ea3d79170b7632d.png)
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解题方法
5 . 已知抛物线
,
,
是C上两个不同的点.
(1)求证:直线
与C相切;
(2)若O为坐标原点,
,C在A,B处的切线交于点P,证明:点P在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fb1a589404b101361fab4a264af920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4adb1a0c5fbcaa7cb61b2febdb7db3.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d031516b8b9572a1973e44004a30493a.png)
(2)若O为坐标原点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb512456bcc994ea2354e9525d3f282.png)
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名校
解题方法
6 . 把抛物线
沿
轴向下平移得到抛物线
.
(1)当
时,过抛物线
上一点
作切线,交抛物线
于
,
两点,求证:
;
(2)抛物线
上任意一点
向抛物线
作两条切线,从左至右切点分别为
,
.直线
交
从左至右分别为
,
两点.试判断
与
的大小关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ebe959b8ff2bbabce1f0f09a36e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fe004046f183e83376ce219c9d1bb0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194b8ab194c7d299d5c3e0f09ec18384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2007972af3341f27fbc32ce62dfce5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/1f30acc34f4ee1077532ae6808af2ab2.png)
(2)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cc25bc9e9c48fd18a60b95b64bb499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920ff4e858ac0ed5e5706bb77bfd5c9e.png)
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21-22高二·湖南·课后作业
7 . 阅读“多知道一点:平面方程”,并解答下列问题:
(1)建立空间直角坐标系,已知
,
,
三点,而
是空间任意一点,求A,B,C,P四点共面的充要条件.
(2)试求过点
,
,
的平面ABC的方程,其中a,b,c都不等于0.
(3)已知平面
有法向量
,并且经过点
,求平面
的方程.
(4)已知平面
的方程为
,证明:
是平面
的法向量.
(5)①求点
到平面
的距离;
②求证:点
到平面
的距离
,并将这个公式与“平面解析几何初步”中介绍的点到直线的距离公式进行比较.
(1)建立空间直角坐标系,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f6f9d8550d619061ab0ba1105ec6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf322f683d50ecd3c7d4d5996122726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
(2)试求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3ea554707fa3fc12fc9de51c94e4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5622d4be6bba8c7a6851dc082ef34fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1f4b53c90e4c31dd35b4bb548c5193.png)
(3)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b163c34a920cb649829c376e7870007a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(4)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e0ae1c14104ee9985e3ba31c604531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(5)①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae715c996c1a6b5e35a3807c671bd6e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
②求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e874a5821372c21a768cd1f5e20536d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c828e62664e7373ed1f6dde8aa9653c.png)
您最近一年使用:0次
名校
解题方法
8 . 某商城进行促销活动,购买某产品的顾客可以参加一次游戏:在一个不透明箱子中放入红、蓝、黄三种颜色的小球各1个,顾客从中有放回地取出小球,直到取出的小球集齐了三种颜色则停止取球.设顾客停止取球时,取过的小球次数为
,
(1)求
;
(2)设
,数列
,求
的通项公式;
(3)顾客停止取球时,取过的小球次数为
,顾客可以获得对应的
元奖金,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beded6e21d93573807f67478c74e7e24.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2984cf03d31b5fa49437a49c393002c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)顾客停止取球时,取过的小球次数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98faa95fff49f487cce3a4fdc58bb067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1269b45b8c9bcb0cada085cd86fd88.png)
您最近一年使用:0次
解题方法
9 . 已知数列
是斐波那契数列,其数值为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
.这一数列以如下递推的方法定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
.数列
对于确定的正整数
,若存在正整数
使得
成立,则称数列
为“
阶可分拆数列”.
(1)已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
.判断是否对
,总存在确定的正整数
,使得数列
为“
阶可分拆数列”,并说明理由.
(2)设数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
,
(i)若数列
为“
阶可分拆数列”,求出符合条件的实数
的值;
(ii)在(i)问的前提下,若数列
满足
,
,其前
项和为
.证明:当
且
时,
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc50612eece655796b752da6b4bc3f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d74fa7fa6330976d7eb8e523a62cd09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cdfd9c3f8933cddb63d87dbe2812994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753358ca020523f27725f5187bb8e988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136a003907c455bfd58875c96c138772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79282bbe9f6408297d6378878c423bec.png)
(i)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)在(i)问的前提下,若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5f894d605847c6df0c4df24cf8e1fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a340cb0e3c456ec64ffdf89d7cd6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.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/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48268fd6d3f92032eb54fbf65c01405.png)
您最近一年使用:0次
名校
解题方法
10 . 已知数列
的前
项和为
,若存在常数
,使得
对任意
都成立,则称数列
具有性质
.
(1)若数列
为等差数列,且
,求证:数列
具有性质
;
(2)设数列
的各项均为正数,且
具有性质
.
①若数列
是公比为
的等比数列,且
,求
的值;
②求
的最小值.
![](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/fc983f1bad03411ae64d84ff7bdf2551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a548095fa134cb2b52721af225cbbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193a0efaa1aa835eb3e061bb25dad4dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
①若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4338dd5d6ac02dbb9d5069eb98f436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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4卷引用:江西省临川第二中学2023-2024学年高二下学期6月月考数学试题
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