23-24高二下·全国·课前预习
1 . 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.
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2 . 已知数列
中,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf34a8a2dbd5d43e95167340b8f1491.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
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3 . 已知等差数列
的首项为
,公差为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
,前
项和为
.
(1)若对
,
为常数k,求k;
(2)若
,用数学归纳法证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0432d8460941037411ded150b3959339.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f282b34cb12ceb853401ede8b9ff7408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a3dab80709d7a4798633a904e1323d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7335c79ec0592fc36288f5135e86c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0432d8460941037411ded150b3959339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132e9579e58d8d5225e2340e1f43adf1.png)
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解题方法
4 . 数列
满足
且
,
,
,
构成等差数列.
(1)试求出所有三元实数组(α,β,γ),使得
为等比数列.
(2)若
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f390f47fa5678c9a165c50fb9dec58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be536a2097ded867adac5edebb79906b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e6820c50fa2aa589de5331d7d5f950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13739ca823d61005798cc3298400c6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad28237c0f9ca65341101d9d7e73e73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
(1)试求出所有三元实数组(α,β,γ),使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4623bc660145c6ff98af7b1753d5357a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
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5 . 用数学归纳法证明:
时,从
到
,等式的左边需要增乘的代数式是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128a2ea4267cfb0388abd887347e2103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-02-11更新
|
312次组卷
|
5卷引用:南阳六校2021-2022学年下学期第一次联考高二理科数学试题
南阳六校2021-2022学年下学期第一次联考高二理科数学试题(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)河南省南阳市第一中学校2023-2024学年高二下学期第一次月考数学试题辽宁省沈阳市第二十中学2023-2024学年高二下学期4月阶段测试数学试卷(已下线)4.4数学归纳法——课堂例题
2024高二·江苏·专题练习
6 . 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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7 . 用数学归纳法证明:
(
)的过程中,从
到
时,
比
共增加了( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c7faffe892fe87ca775ccb6abd52cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de5aeec5fb5769c0a77944312c2267b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a84d7e5d6236009a8be655bd500fd.png)
A.1项 | B.![]() | C.![]() | D.![]() |
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2024-01-30更新
|
956次组卷
|
10卷引用:浙江省杭州第二中学2023-2024学年高二上学期期末考试数学试题
浙江省杭州第二中学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)2023新东方高二上期末考数学01吉林省四平市第一高级中学2023-2024学年高二下学期第一次月考数学试题浙江省舟山市舟山中学2023-2024学年高二下学期4月清明返校测试数学试题辽宁省沈阳市第十中学2023-2024学年高二下学期第一次月考(4月)数学试卷江苏省南京市南京师大附中2024届高三寒假模拟测试数学试题四川省成都市石室中学2024届高三下期三诊模拟考试文科数学试卷四川省成都市石室中学2024届高三下学期三诊模拟考试理科数学试卷
解题方法
8 . 意大利数学家列昂那多斐波那契以兔子繁殖为例,引入“兔子数列”:1,1,2,3,5,8,13,21,34,55,
,即
,
,此数列在现代物理“准晶体结构”、化学等领域都有着广泛的应用.若此数列被2除后的余数构成一个新数列
,则数列
的前2023项的和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b290971efaf65804cc756c038c43fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90bbef6a78ec02b25c350ce2dbd5aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
A.1348 | B.675 | C.1349 | D.1350 |
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9 . 斐波那契数列由意大利数学家斐波那契发现,因以兔子繁殖为例子而引入,故又称为“兔子数列”.斐波那契数列在很多方面都与大自然神奇地契合,小到向日葵、松果、海螺的生长过程,大到海浪、飓风、宇宙系演变,皆有斐波那契数列的身影,充分展示了“数学之美”.斐波那契数列用递推的方式可定义如下:数列
满足:
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef91c948ec388a8c0ed5ecb443c2f76.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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10 . 已知
为数列
的前
项和,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/94b7301fba4344e018aaf591fce320c4.png)
A.存在![]() ![]() | B.![]() |
C.![]() | D.![]() |
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