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解题方法
1 . 已知
,
.记
.
(1)求
的值;
(2)化简
的表达式,并证明:对任意
的,
都能被
整除.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da99f702748f3317e5ce1fe800c1ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aabe9ce0871a0e5956b76a2eb4c4a4df.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3fe529eadda46922f423eacdb88b9c.png)
您最近一年使用:0次
2020-03-17更新
|
2082次组卷
|
16卷引用:江苏省邗江中学2017-2018学年高二下学期期中考试数学(理)试题
江苏省邗江中学2017-2018学年高二下学期期中考试数学(理)试题(已下线)2017-2018学年度下学期高二数学期末备考总动员C卷理科01江苏省南通、徐州、扬州等六市2018届高三第二次调研(二模)测试数学(文理)试题河北省定州中学2018届高三下学期第一次月考数学试题2(已下线)第05章:排列组合及二项式定理(B卷提升篇)-2020-2021学年高二数学下学期同步单元AB卷(苏教版)(已下线)专题6.8 计数原理全章综合测试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)专题11.2 二项式定理(练)-江苏版《2020年高考一轮复习讲练测》2020届江苏省南通市四校联盟高三数学模拟试题2020届江苏省金陵中学、丹阳高级中学、无锡一中高三下学期期初联考数学试题2020届江苏省南京师范大学附中高三下学期第一次模拟考试数学试题(已下线)专题21 计数原理与二项式定理-2021年高考数学二轮优化提升专题训练(新高考地区专用)【学科网名师堂】(已下线)专题8.2 二项式定理的应用-备战2021年高考数学精选考点专项突破题集(新高考地区)(已下线)考点突破16 计数原理-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)(已下线)考点66 二项式定理-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】(已下线)第66讲 二项式定理(已下线)专题16 计数原理(2)
2 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386ed5ab3aa33e27b9dd2af3826e19f1.png)
(1)求
及
的值;
(2)求证:
(
),并求
的值.
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386ed5ab3aa33e27b9dd2af3826e19f1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c315a91bca8863c21b91a050495c74.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98cb5a53391f42581956df5585b5f190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8042dbfe62564fe25de21237029a6619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec29b4de219fb32c8023c9f789d3e78.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1fa7ff012173435df567b200b346f7.png)
您最近一年使用:0次
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3 . 已知函数
,其中
,
.
(1)若
,
,求
的值;
(2)若
,
,求
的最大值;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2726f38fd366d8b8cb2a7791fbc1c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05df47d88bb64fe00c6ef3b9b3699617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ef6aa3dffad6cd3606eea89e483ddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02eadc405a3587bd3499d494e7fad31b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e7f35951f719ea517964e451a65e9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9369885404fbc2428c4c7b476534431e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c9c39efc53af82fec6d9cf76db5afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c41b56cf6b0416029ce7cebccb70ff3.png)
您最近一年使用:0次
2018-07-02更新
|
1297次组卷
|
4卷引用:【全国市级联考】江苏省无锡市2017-2018学年高二下期期末数学(理)试题
【全国市级联考】江苏省无锡市2017-2018学年高二下期期末数学(理)试题(已下线)第6章 计数原理(新文化与压轴30题专练)2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)专题6.8 计数原理全章综合测试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)【全国百强校】江苏省启东中学2018-2019学年高一下学期期中考试(创新班)数学试题
4 . 证明:(1)
;
(2)
;
(3)
;
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f645b4f73e8858fa27e80c4e9c9298d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f092eb3824102475667067361e30bb51.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1cd17e4fd8190533a7eeea2e5650581.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22040e6456047d4817b132f5fff56659.png)
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5 . 设
,
,在集合
的所有元素个数为2的子集中,把每个子集的较大元素相加,和记为
,较小元素之和记为
.
(1)当
时,求
,
的值;
(2)求证:为任意的
,
,
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330a768883271ebe0b692f6c226867a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6862dd3c43647ce7d7935a7d205b54d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:为任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f563f31a226905e5b38ca81078a1af35.png)
您最近一年使用:0次
2018-06-23更新
|
1102次组卷
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2卷引用:【全国百强校】江苏省泰州中学2017-2018学年高二6月月考数学(理)试题
6 . 已知
,
(1)求
的值;
(2)若
且
,求
的值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34482692c04dc24412372cabf5d71f3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315b06e1bcf77dd299f334086a3a2c0d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d028c46e515914407d36fbd607a86f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e65967bdeffe3e70e24c04d8aecae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c4f801be1b2b87caa8a05804156ddf.png)
您最近一年使用:0次
7 . 设
,
,其中
.
(1)当
时,求
的值;
(2)对
,证明:
恒为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfcdfa654b5874be6cff58c317351e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f312c9fb6d2b3a42bc721b5214be4df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a360c7fcb63fe54cde413f4c1859c31.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5f1cb8dd4dc2abe96c68b66d52d5f6.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7b3e0d7e761be5620effba0e1fc40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08585c3f07f917012927a448080e1c7d.png)
您最近一年使用:0次
2018-06-16更新
|
1029次组卷
|
5卷引用:【全国百强校】江苏省海安高级中学2017-2018学年高二6月月考数学(理)试题
【全国百强校】江苏省海安高级中学2017-2018学年高二6月月考数学(理)试题2020届江苏省南通市高三下学期3月开学考试数学试题2020届江苏省苏州市吴中区高三高考模拟数学试题江苏省扬州市江都区大桥高级中学2020届高三下学期学情调研(二)数学试题(已下线)热点11 计数原理-2022年高考数学【热点·重点·难点】专练(新高考专用)
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8 . 某班级共派出
个男生和
个女生参加学校运动会的入场仪式,其中男生倪某为领队.入场时,领队男生倪某必须排第一个,然后女生整体在男生的前面,排成一路纵队入场,共有
种排法;入场后,又需从男生(含男生倪某)和女生中各选一名代表到主席台服务,共有
种选法.(1)试求
和
; (2)判断
和
的大小(
),并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://img.xkw.com/dksih/QBM/2018/5/29/1955791359115264/1958425185583104/STEM/fe9f4c51348241d3b662032dcfa246be.png?resizew=13)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9da2b0e7b9eca965043be2f38a91f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://img.xkw.com/dksih/QBM/2018/5/29/1955791359115264/1958425185583104/STEM/45dd36f2173e44758f12e994ffec5f46.png?resizew=20)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48c33f258a1461112553fb442e9103b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9da2b0e7b9eca965043be2f38a91f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
您最近一年使用:0次
2018-06-02更新
|
1027次组卷
|
4卷引用:江苏省扬州市邗江区2017-2018学年高二下学期期中考试数学(理)试卷
江苏省扬州市邗江区2017-2018学年高二下学期期中考试数学(理)试卷江苏省苏州市高新区第一中学2018-2019学年高二下学期5月阶段调研理科数学试题(已下线)第02讲 排列-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第二册)(已下线)6.2.2 排列数(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第三册)
9 . 请阅读:当
时,在等式
的两边对
求导,得
,利用上述方法,试由等式
(
,正整数
).
(1)证明:
;(注:
)
(2)求
;
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96197741cee878c94318b9d840b46a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c78795768ff8d31eb51ec0b17f9f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d7664675da7c27b90e54cb7887eb2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd19918a18603b334b3faa77f2b2ace2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82add3c2f480d0c092f497a32c6da3e9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc9b7fa551545192e12b1371f34de05.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3772441403ffd20d525b6b529a5108d7.png)
您最近一年使用:0次
2018-04-27更新
|
1330次组卷
|
3卷引用:【全国区级联考】江苏省徐州市铜山区2017-2018学年高二下学期期中考试数学(理)试题
【全国区级联考】江苏省徐州市铜山区2017-2018学年高二下学期期中考试数学(理)试题江苏省涟水中学2018-2019学年高二5月月考数学(理)试题(已下线)第六章 计数原理(基础卷)-《阳光测评》2020-2021学年高二数学单元提升卷(人教A版2019选择性必修第三册)