2024高二·江苏·专题练习
1 . 已知n为正整数,试比较
与
的大小 .
当
时,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
;
当
时,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152a6437e4a84f7921ed58d03f6bc05f.png)
;
当
时,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e094ab289cd1fb2cf6f184fd3bc85075.png)
;
当
时,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152a6437e4a84f7921ed58d03f6bc05f.png)
;
当
时,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
;
当
时,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
;
猜想:当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b69e2d75d77209cc043d994ba9d446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c166c64cef20a5456749141f67ff23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a593a2690bd10cfb39d6f4053353ef57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0039416bef7a76e050c6cb45b2f1a848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152a6437e4a84f7921ed58d03f6bc05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d14adc519a7b15f2f8db95628700eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fae9ba4288074b3a729bfc169ea6212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e094ab289cd1fb2cf6f184fd3bc85075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68619a119152e9ccb031fae3207a1e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f73dbfb41226966714dc4fe38cf67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152a6437e4a84f7921ed58d03f6bc05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34cc00f4c2de561af4bb7e8a4c2868ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa552f8a88856899937b1fc68e3ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0936bd6925580c3ddcbfb2252a08b4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68de14f7f30d6b161e556c02544a6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
猜想:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5d0a73f50b3e4583f1c1b6d6bf0d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb630633169e90a319bb75012eaeda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
您最近一年使用:0次
2023高二上·江苏·专题练习
2 . 有下列命题:
;使用数学归纳法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855095e11c24068738b6f44233f74aaa.png)
您最近一年使用:0次
3 . 设
,用数学归纳法证明:
是64的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1351575c790756b8296032e865b81d2.png)
您最近一年使用:0次
2024-03-16更新
|
93次组卷
|
7卷引用:4.4 数学归纳法(2)
(已下线)4.4 数学归纳法(2)(已下线)专题4.4 数学归纳法(2个考点四大题型)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)苏教版(2019)选择性必修第一册课本习题 习题4.4(已下线)5.5数学归纳法(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)(已下线)5.5 数学归纳法(2知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)(已下线)4.4 数学归纳法(6大题型)精练-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册) (已下线)4.4数学归纳法——课后作业(巩固版)
4 . 用数学归纳法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dc4c84b0e18b2da77fea013ab52d1d.png)
您最近一年使用:0次
2023-10-11更新
|
331次组卷
|
5卷引用:4.4 数学归纳法(6大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)
(已下线)4.4 数学归纳法(6大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)北师大版(2019)选择性必修第二册课本习题第一章复习题(已下线)1.5 数学归纳法7种常见考法归类(2)(已下线)5.5 数学归纳法(2知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)(已下线)4.4 数学归纳法(6大题型)精讲-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)
5 . 用数学归纳法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce85ffef484bfd6e3fb956b2211581a.png)
您最近一年使用:0次
2023-10-11更新
|
216次组卷
|
6卷引用:4.4 数学归纳法(1)
(已下线)4.4 数学归纳法(1)北师大版(2019)选择性必修第二册课本习题 习题1-5(已下线)5.5数学归纳法(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)1.5 数学归纳法7种常见考法归类(1)(已下线)4.4 数学归纳法(6大题型)精练-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册) (已下线)4.4数学归纳法——课后作业(基础版)
6 . 用数学归纳法证明:
能被
整除(
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c908bdaed25d5cb0ceb24f6c871b850c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
您最近一年使用:0次
2023-10-10更新
|
137次组卷
|
8卷引用:4.4 数学归纳法(2)
(已下线)4.4 数学归纳法(2)北师大版(2019)选择性必修第二册课本习题第一章§5 数学归纳法(已下线)5.5数学归纳法(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)1.5 数学归纳法7种常见考法归类(1)(已下线)5.5 数学归纳法(2知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)(已下线)4.4 数学归纳法(6大题型)精讲-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册) (已下线)4.4数学归纳法——课后作业(基础版)北师大版(2019)选择性必修第二册课本例题§5 数学归纳法
解题方法
7 . 用数学归纳法证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77a0c62b5cddf3bf1634673e2f87f93.png)
您最近一年使用:0次
2023-09-25更新
|
92次组卷
|
5卷引用:4.4 数学归纳法(1)
(已下线)4.4 数学归纳法(1)苏教版(2019)选择性必修第一册课本例题4.4 数学归纳法(已下线)5.5数学归纳法(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)1.5 数学归纳法7种常见考法归类(1)(已下线)4.4数学归纳法——课后作业(巩固版)
23-24高二上·上海·课后作业
8 . 设数列
的各项均为正整数,且
.记
.如果对于所有的正整数
均有
.
(1)求
,
,
,
,
;
(2)猜想
的通项公式,并加以证明.
![](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/2efba990f1fca3fe00fb5e0a7fff0bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f87771015d6b6a42eeb686cf63249f8.png)
(1)求
![](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/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27182444d3da4003680f07ec299087c.png)
(2)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
您最近一年使用:0次
2023-09-12更新
|
199次组卷
|
7卷引用:4.4 数学归纳法(2)
(已下线)4.4 数学归纳法(2)(已下线)专题4.4 数学归纳法(2个考点四大题型)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)(已下线)4.4 数学归纳法(已下线)5.5数学归纳法(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)1.5 数学归纳法7种常见考法归类(1)(已下线)4.4 数学归纳法(6大题型)精讲-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册) (已下线)4.4数学归纳法——课后作业(巩固版)
23-24高二上·上海·课后作业
9 . 已知数列
满足
尝试通过计算数列
的前四项,猜想数列
的通项公式,并用数学归纳法加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bca90a6805973ae10f644ae270510f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
23-24高二上·上海·课后作业
10 . (1)依次计算下列各式的值:
,
,
,
.
(2)根据第(1)题的计算结果,猜想
(
为正整数)的表达式,并用数学归纳法证明相应的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5296c0056db0e2b5331c9b9a6d45962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6898c8129d4cdb8ae988854f553723c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c1db1861753db975385da6ec85f743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9af7498b656097fe51a3d5ff044dd48.png)
(2)根据第(1)题的计算结果,猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e30da1db1ed26dec3eacb75d5471f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次