名校
1 . 定义
为有限实数列{an}的波动强度.
(1)求数列1,4,2,3的波动强度;
(2)若数列a,b,c,d满足(a﹣b)(b﹣c)>0,判断f(a,b,c,d)≤f(a,c,b,d)是否正确,如果正确请证明,如果错误请举出反例;
(3)设数列a1,a2,…,an是数列1+21,2+22,3+23,…,n+2n的一个排列,求f(a1,a2,…,an)的最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c5364b3ac495babdd166ad1f501337.png)
(1)求数列1,4,2,3的波动强度;
(2)若数列a,b,c,d满足(a﹣b)(b﹣c)>0,判断f(a,b,c,d)≤f(a,c,b,d)是否正确,如果正确请证明,如果错误请举出反例;
(3)设数列a1,a2,…,an是数列1+21,2+22,3+23,…,n+2n的一个排列,求f(a1,a2,…,an)的最大值,并说明理由.
您最近一年使用:0次
2 . 已知数列
,具有性质P:对任意
(
)
与
,两数中至少有一个是该数列中的一项,
为数列
的前
项和.
(1)分别判断数列0,1,3,5与数列0,2,4,6是否具有性质P:
(2)证明:
且
;
(3)证明:当
时,
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab0618ddda6e7eeba8a14c2655833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb18c6dbf63138dd5cf7cae946c106e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae331839bce8f3c14d7efd7f9d8915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)分别判断数列0,1,3,5与数列0,2,4,6是否具有性质P:
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1fe4c51169a32e05e4be4acb3d1f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc31cec2f263c4fbed39962f960daef.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd49c085be2656091b79da53f010a1a.png)
您最近一年使用:0次
2021-03-25更新
|
942次组卷
|
3卷引用:考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮
2020高三·上海·专题练习
3 . 设
,
满足递推关系
,初值条件
.令
,即
,令此方程的两个根为
、
,若
,则有
(其中
),若
,则有
(其中
).
证明:如果数列
满足下列条件:已知
的值,且对于
,都有
(其中
、
、
、
均为常数,且
,
,
),那么,可作特征方程
.
(1)当特征方程有两个相同的根
(称作特征根)时,若
,则
,
;若
,则
,
其中
,
.
特别地,当存在
使
时,无穷数列
不存在;
(2)当特征方程有两个相异的根
、
(称作特征根)时,则
,
,其中
,
(其中
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11afb610afef770a3927d3f43423004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77320e643bdaf88ba8ae88be8dd4dfea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6bcfdd99dc17c7849095ce1e9f2530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f76bb60e54410f2146349c1b8a62859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f333263260646c494225db8a7476c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b7f78550b99977a4c5a9600f26936b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e127a8a6258284b9289b2f5ce51b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114fd36d5f85fc927344a507fee158f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abd8d57d7deb4c3cb59a2f8bebaa7d1.png)
证明:如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3baf2e44c62016d2e519a5ee7c13ec19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992f1c63efb257ea61c2c2515400ceb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790fd1b4fe3a98055b08bcb9d332f072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68634f6b6ca282c408e075809c6789b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c24b5fa851cae6fc9d289412fef919.png)
(1)当特征方程有两个相同的根
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47769ca08edfa79fc200b9f37d197335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3ac862051caf821465580fdebc5e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3d56df807ed171127cfe53d68c9e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58d13f3186462f976d4921066cc3783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea90e8ed89e3c43a0bd1cb1a654c81c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
特别地,当存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c55f3b870ec43e1c778b2acd532e718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390981c620bdce40320fa196cc75f85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当特征方程有两个相异的根
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1306b4a37f5c966737f4c07c6b40262e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6052302df2bb03ecb01b6713bc7ec291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7129d04a40722e38b656a126c2267575.png)
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2021-01-07更新
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746次组卷
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4卷引用:专题10 数列(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)
(已下线)专题10 数列(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)(已下线)重难点02 数列(特征根法与不动点法)-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)第4章 数列 单元综合检测(难点)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)专题10 数列通项公式的求法 微点8 不动点法
4 . 对于由m个正整数构成的有限集
,记
,特别规定
,若集合M满足:对任意的正整数
,都存在集合M的两个子集A、B,使得
成立,则称集合M为“满集”,
(1)分别判断集合
与
是否为“满集”,请说明理由;
(2)若
由小到大能排列成公差为d(
)的等差数列,求证:集合M为“满集”的必要条件是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14f5fdf0e4f9de36f08402dd96d237e.png)
或2;
(3)若
由小到大能排列成首项为1,公比为2的等比数列,求证:集合M是“满集”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e495e34870eb6eef8486f88e567c7e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9cd59e58555bfc92257ba31d16794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44aed8cc107aecae26873891bfdc5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf084cdb896062c63e919adf38352d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01a90899f08d43e7f1b945b96aae753.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4804e8c356d6aa5b0d645fed77fec88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5d150c4bf3836b14db9cd1017aeacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e789387bf82c893b83cb8f2007f060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14f5fdf0e4f9de36f08402dd96d237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f0913464ddee73888f859ec6ad1696.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
您最近一年使用:0次
2020-12-27更新
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822次组卷
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4卷引用:考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮
(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮上海市松江区2021届高三上学期期末(一模)数学试题上海市松江区2021届高三高考数学一模试题北京市人大附中朝阳学校2020-2021学年高二下学期数学统测试题
解题方法
5 . 已知函数
.
(1)证明:
时,
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9a6a0ad0a5ee53205ac42a6261fa03.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b9a926eb1876d017ce1198e32efec6.png)
您最近一年使用:0次
2020-12-14更新
|
1688次组卷
|
7卷引用:专题04 利用导数证明不等式 第一篇 热点、难点突破篇(讲)- 2021年高考二轮复习讲练测(浙江专用)
(已下线)专题04 利用导数证明不等式 第一篇 热点、难点突破篇(讲)- 2021年高考二轮复习讲练测(浙江专用)(已下线)专题15 函数、数列、三角函数中大小比较问题(讲)-2021年高三数学二轮复习讲练测 (新高考版)(已下线)专题04 利用导数证明不等式(讲)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》(已下线)第三章 重点专攻二 不等式的证明问题(讲)安徽省池州市东至县2020-2021学年高三上学期12月大联考数学(文)试题安徽省全省名校实验班2020-2021学年高三上学期大联考文科数学试题江苏省苏州市张家港市2022-2023学年高三上学期1月期末数学试题
名校
解题方法
6 . 若实数列
满足条件
,
、
、
,则称
是一个“凸数列”.
(1)判断数列
和
是否为“凸数列”?
(2)若
是一个“凸数列”,证明:对正整数
、
、
,当
时,有
;
(3)若
是一个“凸数列”,证明:对
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8414472e2121e1796eb40408d820053a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9c3bf014213b50c1ce94d96f07dbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da367d9a7896e0eb1b8fdc91918f19f2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/cf09cb20d3ac1ee84b63893098f56f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97bb4c969108ebef4ebadd5acc5ca4.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2400554b00420e4f4040f3b10e1bf73f.png)
您最近一年使用:0次
7 . 已知数列
,
,
,若数列
、
都是等比数列,公比分别是
、
,设
是数列
的前
项和,数列
是
的零点按从小到大的顺序排成的数列.
(1)求数列
的通项公式,并证明:
;
(2)证明:
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4e1236d7dc0366d9523d0cbb426be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc0d9ecf4a552405584ef092db53508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dc43b8d11d5462e4b525dd7b03bcfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e79faea88f4bf336ea6cae4b14e5f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4e2aba0ca1d981cb845d5f58257a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53aaf8438a97b289940956774fd7701.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e31dda3a56eb4c92347b3ea80143fc6.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293f50856f92a18be3301a658781a8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc9e71aae5fbed265ba31ab9b5cfc78.png)
您最近一年使用:0次
19-20高二·全国·单元测试
解题方法
8 . 冠状病毒是一个大型病毒家族,已知可引起感冒以及中东呼吸综合征(
)和严重急性呼吸综合征(
)等较严重疾病.而今年出现在湖北武汉的新型冠状病毒(
)是以前从未在人体中发现的冠状病毒新毒株.人感染了新型冠状病毒后常见体征有呼吸道症状、发热、咳嗽、气促和呼吸困难等.在较严重病例中,感染可导致肺炎、严重急性呼吸综合征、肾衰竭,甚至死亡.某医院为筛查冠状病毒,需要检验血液是否为阳性,现有n(
)份血液样本,有以下两种检验方式:方式一:逐份检验,则需要检验n次.方式二:混合检验,将其中k(
且
)份血液样本分别取样混合在一起检验.若检验结果为阴性,这k份的血液全为阴性,因而这k份血液样本只要检验一次就够了,如果检验结果为阳性,为了明确这k份血液究竟哪几份为阳性,就要对这k份再逐份检验,此时这k份血液的检验次数总共为
.假设在接受检验的血液样本中,每份样本的检验结果是阳性还是阴性都是独立的,且每份样本是阳性结果的概率为p(
).现取其中k(
且
)份血液样本,记采用逐份检验方式,样本需要检验的总次数为
,采用混合检验方式,样本需要检验的总次数为
.
(1)若
,试求p关于k的函数关系式
;
(2)若p与干扰素计量
相关,其中
(
)是不同的正实数,满足
且
(
)都有
成立.
(i)求证:数列
等比数列;
(ii)当
时,采用混合检验方式可以使得样本需要检验的总次数的期望值比逐份检验的总次数的期望值更少,求k的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e131f089036a9be6df197930c58b951f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed377f70fd55d20da3c659e95bce0dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ee707e1e8147f26a8b2f569072c4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699dfd96d64e59252e384847629c7a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699dfd96d64e59252e384847629c7a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d388f32e318b0c7f2d9d10a5c6525b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f1ce5bbcc57f96d99d2c4f27cc2e42.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd314aee9f06722598766b752fa1e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb00792538f7ae7cd3303b465fada7a.png)
(2)若p与干扰素计量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff11bb9d064693dae7fd5619fbddc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae39aced7d238ce77a67910f6853227.png)
(i)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/593f989a1d3977debae9a3010616ded5.png)
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2020-08-28更新
|
2149次组卷
|
7卷引用:专题7.1 概率中的应用问题 -玩转压轴题,进军满分之2021高考数学选择题填空题
(已下线)专题7.1 概率中的应用问题 -玩转压轴题,进军满分之2021高考数学选择题填空题(已下线)第51讲 概率与统计综合问题-2022年新高考数学二轮专题突破精练(已下线)专题9-1 概率与统计及分布列归类(理)(讲+练)-2(已下线)专题8-2分布列综合归类-2(已下线)第三章统计案例单元测试(基础版) -突破满分数学之2019-2020学年高二数学(理)重难点突破(人教A版选修2-3)(已下线)第二章随机变量及其分步单元测试(巅峰版) -突破满分数学之2019-2020学年高二数学(理)课时训练(人教A版选修2-3)(已下线)综合测试卷(巅峰版) -突破满分数学之2019-2020学年高二数学(理)课时训练(人教A版选修2-3)
9 . 已知数列
的首项
,
为前
项和,若数列
满足:对任意正整数
,
,当
时,
总成立,则称数列
是“
数列”.
(1)若
是公比为3的等比数列,试判断
是否为“
数列”,说明理由;
(2)若
是公差为
的等差数列,且是“
数列”,求实数
的值;
(3)若数列
既是“
数列”,又是“
数列”,求数列
的通项公式.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52eecd38954cd0ca3fb26328a39bb859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa23c1bcee5cdc55dff21f1ad06d5f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e0fcb1c9a990f1d58e7e0e74017beb.png)
(1)若
![](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/d789e6134104e5b12f6014aa4928ca96.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8f4267df6060a6cc277073d6c2d248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d789e6134104e5b12f6014aa4928ca96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8f4267df6060a6cc277073d6c2d248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
解题方法
10 . 已知
(
)
(1)若
对
恒成立,求实数a范围;
(2)求证:对
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ae3a06e2db61ce958f143eb7f7390b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(2)求证:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5141a5b907f5ff11bbd7cacbd7b5db3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4d16e77a13cb72c849cac26c8ae54e.png)
您最近一年使用:0次
2020-07-25更新
|
1083次组卷
|
4卷引用:专题05 数列-【备战高考】2021年高三数学高考复习刷题宝典(压轴题专练)
(已下线)专题05 数列-【备战高考】2021年高三数学高考复习刷题宝典(压轴题专练)四川省成都市树德中学2021-2022学年高三上学期11月阶段性测试(期中)数学(理)试题四川省成都市第七中学2020年普通高等学校招生统一热身考试文科数学试题四川省成都市第七中学2020届高三高考(7.2)热身考试文科数学试题