1 . 设正整数
,集合
,
是集合P的3个非空子集,记
为所有满足:
的有序集合对(A,B,C)的个数.
(1)求
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf41b2793efa0b332fe039341370ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02aac9ee9a68059dd93af7d6e7517561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://img.xkw.com/dksih/QBM/2019/7/11/2244569768509440/2244614889267200/STEM/76f2937c00b84d4eaaa52d7c80e4996e.png?resizew=213)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
名校
2 . 已知
的展开式中没有常数项,则n的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f28accda430f42cebc34e837e97ec59.png)
A.6 | B.7 | C.8 | D.9 |
您最近一年使用:0次
2019-05-17更新
|
694次组卷
|
2卷引用:【全国百强校】江苏省海安高级中学2018-2019学年高一下学期期中考试数学试题1
3 . 设
,
.
(1)求
的值;
(2)化简
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dcbfc512c5d50486268eca3487eac86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b67d04a888499aa527048029e06538.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a684a84687611e5ab8471f11f2bb9c.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cffd7ed8e5f410f5f7cdd2e6eed91.png)
您最近一年使用:0次
4 . 已知数列
的通项公式为
,
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
.
(1)求
,
的值;
(2)求证:对任意正整数
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db219ef0253b108b6001161c5d57f689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0ab04a8d3b5029d3d9a7122fcb6c35.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)求证:对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df6a9d2e81772b08ae2735038565159.png)
您最近一年使用:0次
名校
5 . 已知函数
.
(1)当
时,求展开式中系数的最大项;
(2)化简
;
(3)定义:
,化简:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7ad2d23bfd6c25425ea9562c7c9baa.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b24ed5cfa084044fffc3795912ade.png)
(3)定义:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2955a1ae6ca7b3a7c9fd5b3e7bdc09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2526a87f15b0bd2fe90aa9ef330b7e.png)
您最近一年使用:0次
2018-12-31更新
|
2269次组卷
|
4卷引用:【市级联考】江苏省南通市如皋2018-2019学年高二上学期教学质量调研(三)数学(理科)试题
【市级联考】江苏省南通市如皋2018-2019学年高二上学期教学质量调研(三)数学(理科)试题江苏省连云港市海头高级中学2019-2020学年高二下学期期初考试数学试题江苏省扬州大学附中2019-2020学年高二下学期阶段检测数学试题(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)
6 . 设
且
,集合
的所有
个元素的子集记为
.
(1)当
时,求集合
中所有元素之和
;
(2)记
为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
中最小元素与最大元素之和,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110cb59a3406578a01263b76e5325273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44417455b9cc30693d09cbcfe4ed97c3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44417455b9cc30693d09cbcfe4ed97c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a584b6ad5577ab3e2d22caf23e3c32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835e8c3900cb61bc8ddc313d5ce2253d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bac6aad5d92e36b11607f1c9c9640bd.png)
您最近一年使用:0次
2018-12-13更新
|
1314次组卷
|
5卷引用:江苏省南通市西亭高级中学2019-2020学年高三下学期学情调研数学试题
名校
7 . 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
【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【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)
8 . 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)
名校
9 . 请阅读:在等式
(
)的两边对
求导得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9d6347e388c16e07701a24f16649c7.png)
,化简后得等式
.
请类比上述方法,试由等式
(
,
且
).
(1)证明:
(注:
);
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32eac4b7f177c041219fab18de973c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9d6347e388c16e07701a24f16649c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91762cbdb95aa38b3780b3a582ad600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cb17b07a5d34718ddb69311352f5bf.png)
请类比上述方法,试由等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188636a9b1cf547f2bcd49faf20dbbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf343eb5b7e46b39c2135be4830d777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2955a1ae6ca7b3a7c9fd5b3e7bdc09.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089a65a7ed0873075b5d6ecb5a3799e.png)
您最近一年使用:0次