1 . 数列
满足
,
(
).
(1)计算
,
,猜想数列
的通项公式并证明;
(2)求数列
的前n项和;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be815a472dbc3112591a3c311750b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109c4b28048ec9e72ba8ecd6311d9f7e.png)
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解题方法
2 . 已知数列
的前
项和为
,
,
.
(1)计算:
,
,
,并猜想数列
的通项公式;
(2)用数学归纳法来证明(1)中猜想;
(3)记
,求
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ec6b904bcb377349b4bf675acb01b7.png)
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)用数学归纳法来证明(1)中猜想;
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee26dcc81018cd00f2d6956fb85be7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda6cdf0b6787bbe783c9fbcf0649f20.png)
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名校
解题方法
3 . 已知数列
满足
,设该数列的前
项和为
,且
,
,
成等差数列.
(1)用数学归纳法证明:
(
是正整数);
(2)求数列
的通项公式.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebadf2b3ec3dc92cd902eff76085ad46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39835887158fcba559fdfe35ebb5c63.png)
(1)用数学归纳法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8adf14f70232202f11d2bb28a8465b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2024高二·江苏·专题练习
4 . 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)
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名校
5 . 用数学归纳法证明:对于任意正整数
都有:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aac2560569ed95856b84b5a0f6b4447.png)
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2024-01-18更新
|
277次组卷
|
4卷引用:上海市上海中学2023-2024学年高二上学期期末考试数学试题
上海市上海中学2023-2024学年高二上学期期末考试数学试题(已下线)1.5数学归纳法(分层练习,7大考点)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)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)
2023高二上·江苏·专题练习
6 . 有下列命题:
;使用数学归纳法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855095e11c24068738b6f44233f74aaa.png)
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7 . 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)
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2024-03-16更新
|
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7卷引用:苏教版(2019)选择性必修第一册课本习题 习题4.4
苏教版(2019)选择性必修第一册课本习题 习题4.4(已下线)4.4 数学归纳法(2)(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)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(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)
8 . 证明:凸n边形的对角线的条数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3b5b9f04c9dbbeaafe519263899779.png)
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9 . 用数学归纳法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dc4c84b0e18b2da77fea013ab52d1d.png)
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5卷引用:北师大版(2019)选择性必修第二册课本习题第一章复习题
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)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)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)
10 . 用数学归纳法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce85ffef484bfd6e3fb956b2211581a.png)
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6卷引用:北师大版(2019)选择性必修第二册课本习题 习题1-5
北师大版(2019)选择性必修第二册课本习题 习题1-5(已下线)4.4 数学归纳法(1)(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)