21-22高二·江苏·课后作业
名校
1 . 对于不等式
,某同学用数学归纳法证明的过程如下:
①当
时,
,不等式成立;
②假设当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
时,不等式成立,即
,
则当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287a03d6baf51d1ca7bbbc700e8fcf9d.png)
.
故当
时,不等式成立.
则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788f0aeda158acbd74806049081c2d89.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04af9509459b72021abbaa87f272db.png)
②假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fc82353331abee0828dee9b38c08f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f6b1237dd038b15a2bce8d68bb7177.png)
则当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287a03d6baf51d1ca7bbbc700e8fcf9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c228487e3189a83888e5dd56a05b76.png)
故当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
则下列说法错误的是( )
A.过程全部正确 | B.![]() |
C.![]() | D.从![]() ![]() |
您最近一年使用:0次
2021-11-21更新
|
229次组卷
|
4卷引用:4.4 数学归纳法-2021-2022学年高二数学尖子生同步培优题典(苏教版2019选择性必修第一册)
(已下线)4.4 数学归纳法-2021-2022学年高二数学尖子生同步培优题典(苏教版2019选择性必修第一册)1.5数学归纳法检测A卷(基础巩固)1.5数学归纳法测试卷江西省宜春市丰城市东煌学校2023-2024学年高二下学期4月期中考试数学试题
名校
2 . 已知定义域为
的函数
同时满足:
①对于任意的
,总有
;
②若
,
,
,则有
;③
;
以下命题中正确的命题的序号为__________ .(请写出所有正确的命题的序号)
(1)
;
(2)函数
的最大值为
;
(3)函数
对一切实数
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aae852c3129efc16934aefc54201f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cd2fe62ffe3caa1c6f7976851c9dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2f51cd760aeff9365b51e9a85b41e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a55141a7ecd250e67d1228bdc3a1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
以下命题中正确的命题的序号为
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d3c756a52c9185ae6d02d9b9312f29.png)
您最近一年使用:0次
2019高二下·全国·专题练习
3 . 对于不等式
<n+1(n∈N*),某同学用数学归纳法证明的主要过程如下:
(1)当n=1时,
<1+1 ,不等式成立;
(2)假设当n=k(k∈N*)时,不等式成立,有
<k+1,即k2+k<(k+1)2,则当n=k+1时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a302257faaf216c39819d79b869c7233.png)
=
<
=
=(k+1)+1,所以当n=k+1时,不等式也成立.
则下列说法中正确的有_____________ . (填出所有正确说法的序号)
①证明过程全部正确;②n=1的验证不正确;③n=k的归纳假设不正确;④从n=k到n=k+1的推理不正确.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724c1777008ea406b39b467c3137d24f.png)
(1)当n=1时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af09066970c5b676e38185230a1a3f18.png)
(2)假设当n=k(k∈N*)时,不等式成立,有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5016ff719ec8a7dabc256543207b7858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a302257faaf216c39819d79b869c7233.png)
=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0c664271bd507465c234ac71b64c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad26aa655a18525316d38c6effb9810f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6b06e071dc81e93df97b29bcdf9c1e.png)
则下列说法中正确的有
①证明过程全部正确;②n=1的验证不正确;③n=k的归纳假设不正确;④从n=k到n=k+1的推理不正确.
您最近一年使用:0次
4 . 给出下列命题:
用反证法证明命题“设a,b,c为实数,且
,
,则
,
,
”时,要给出的假设是:a,b,c都不是正数;
若函数
在
处取得极大值,则
或
;
用数学归纳法证明
,在验证
成立时,不等式的左边是
;
数列
的前n项和
,则
是数列
为等比数列的充要条件;
上述命题中,所有正确命题的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee08def7a24d4255453ad40a77cd4e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd92e0bbdc7a5fd3d604160cf4306ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae018fde08edf0539089f98c17e11ff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19bce4c604450307f40dcbd6a9ca6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d0ce4e36a37c22267c03b54bd5ba3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f8c4d135ae1aa3911dec9d086b489d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2600a54b7bf3f79aaec7d49a47f6b4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36a91b78ea833d5b09c11366324a845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67312d6fbde2db992b25a11f4ec102b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82e415812cca9545611c0faa0c01b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052c6cf4517966ecebd39354490b1723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c9d7f7f9a3e9ec476f5cf7fda97c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb989bea4883060e495e03e709593361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8b8edd94bc4d5d517ec77e56800e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f13167b6a291eeb91bd9a796745f6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d493ee368a6be6e8de57368520c8cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
上述命题中,所有正确命题的序号为
您最近一年使用:0次
5 . 对于不等式
,某学生用数学归纳法的证明过程如下:
①当
时,
,不等式成立
②假设
,
时,不等式成立,即
,则
时,
,∴当
时;不等式成立.
关于上述证明过程的说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56651c7bb81b1237ae48b0717fac27fb.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fae4f95b1eb365c6e7c6737309e37dc.png)
②假设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c30f669ea79445ffe9392f4e8a16ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485f243d9905a69022035e85bf8648ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b97365f145bace419e90d55726b733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
关于上述证明过程的说法正确的是( )
A.证明过程全都正确 |
B.当![]() |
C.归纳假设正确 |
D.从![]() ![]() |
您最近一年使用:0次
6 . 已知数列
满足
,且
(
为正整数),利用数列的递推公式猜想数列
的通项公式为
.下面是用数学归纳法的证明过程:
(1)当
时,
满足
,命题成立;
(2)假设
(
为正整数)时命题成立,即
成立,则当
时,由
得
,即
是以
为首项,1为公差的等差数列,所以
,即
,所以
,命题也成立.由(1)(2)知,
.
判断以下评述:( )
![](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/d379316dbb3a43e30f166865e0b2b9e8.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/4b648c181bcdc3d2615ce69dfdaba838.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b648c181bcdc3d2615ce69dfdaba838.png)
(2)假设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e2ee54ed7432592b537ac501a38f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d379316dbb3a43e30f166865e0b2b9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3467643d35475b81e68113b368e6f869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2239ce26f47c223c00954290dd3aa85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6729f8558726a382e15eb3f147df2f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b648c181bcdc3d2615ce69dfdaba838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a193f04226baa51605ca3de04c35c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b648c181bcdc3d2615ce69dfdaba838.png)
判断以下评述:( )
A.猜想正确,推理(1)正确 | B.猜想不正确 |
C.猜想正确,推理(1)(2)都正确 | D.猜想正确,推理(1)正确,推理(2)不正确 |
您最近一年使用:0次
23-24高二下·全国·课前预习
7 . 判断正误,正确的写正确,错误的写错误
(1)应用数学归纳法证明数学命题时.
(2)用数学归纳法进行证明时,要分两个步骤,缺一不可.
(3)推证n=k+1时可以不用n=k时的假设.
您最近一年使用:0次
8 . 已知命题1+2+22+…+2n-1=2n-1及其证明:
(1)当n=1时,左边=1,右边=21-1=1,所以等式成立;
(2)假设n=k时等式成立,即1+2+22+…+2k-1=2k-1成立,则当n=k+1时,1+2+22+…+2k-1+2k=
=2k+1-1,所以n=k+1时等式也成立.
由(1)(2)知,对任意的正整数n等式都成立.
判断以上评述( )
(1)当n=1时,左边=1,右边=21-1=1,所以等式成立;
(2)假设n=k时等式成立,即1+2+22+…+2k-1=2k-1成立,则当n=k+1时,1+2+22+…+2k-1+2k=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69ac2bb8c9eb9b5fb0c2888edab4186.png)
由(1)(2)知,对任意的正整数n等式都成立.
判断以上评述( )
A.命题、推理都正确 | B.命题正确、推理不正确 |
C.命题不正确、推理正确 | D.命题、推理都不正确 |
您最近一年使用:0次
2018-02-25更新
|
415次组卷
|
5卷引用:高中数学人教A版选修2-2 第二章 推理与证明 2.2.2 反证法(1)
高中数学人教A版选修2-2 第二章 推理与证明 2.2.2 反证法(1)苏教版(2019) 选修第一册 必杀技 第四章 4.4 数学归纳法苏教版(2019) 选修第一册 一蹴而就 第4章 4.4 数学归纳法(已下线)4.4 数学归纳法(课堂培优)-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)人教B版(2019) 选修第三册 必杀技 第五章 5.5 数学归纳法
9 . 在数学归纳法证明等式“
”时,某学生证明如下:(ⅰ)当
时,左边
,右边
,
原等式成立;(ⅱ)假设
时等式成立,即
,那么当
时,
,即当
时,等式也成立.根据(ⅰ)、(ⅱ)可以判断,等式对任意
都成立.评价该学生的证明情况:______ (选填“正确”或“错误”).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970669da5005b273c26df0fc6f6b049f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90bae886c8ab958aa4c693bf8e0627d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4e2459d0cf0a99b211d6f197b71004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb5e65c7be63c3454a752869cfe56fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d9155e51b41ffef5556ecd5a9e1885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
您最近一年使用:0次
2019-11-09更新
|
87次组卷
|
2卷引用:沪教版 高二年级第一学期 领航者 第七章 7.4数学归纳法