名校
解题方法
1 . 已知
三点共线,其中
,点
关于
轴的对称点为点
,给出下面四个结论:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
不可能 为等边三角形;
②设
,则当
最大时,
;
③
;
④当AB不与
轴垂直时,直线
过定点.
其中正确结论的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57988361c24c97a8879a79da797f791b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4388577dc452ba9d9caf47d81e6f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2e41c64ac5508a9ba27b697122d6d5.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1a8c1ddf518d896001b32fa594576b.png)
④当AB不与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
其中正确结论的个数为( )
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
名校
解题方法
2 . 在现实生活中,一个符合实际的函数模型经常是将不同的函数组合得到的,如听音乐家演奏音乐时,我们听到的声音常常就是多种不同乐器产生的声波叠加的结果.在学习了向量和三角函数后,人大附中某研学小组利用所学知识研究若干振幅相同,同频同向的简谐波叠加后,得到新的简谐波的振幅和初相规律,该小组把
(N为正整数)叠加,研究
中的
和
,其中
.
(1)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
(2)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2073aefa188a89d515b9d32de5d89c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e289d2f03b9a42c8f61858f1c3b32e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52d236ed8d14f8135a0a63d41a351fe.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb55d413f1ab722e17747c8e99f6c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722068b39032dd59c01afdba985d65be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
您最近一年使用:0次
名校
3 . 已知
为
维向量,若
,则称
为可聚向量.对于可聚向量
实施变换
:把
的某两个坐标
删除后,添加
作为最后一个坐标,得到一个
维新向量
,如果
为可聚向量,可继续实施变换
,得到新向量
,……,如此经过
次变换后得到的向量记为
.特别的,二维可聚向量变换后得到一个实数.若向量
经过若干次变换后结果为实数,则称该实数为向量
的聚数.
(1)设
,直接写出
的所有可能结果;
(2)求证:对于任意一个
维可聚向量
,变换
总可以进行
次;
(3)设
,求
的聚数的所有可能结果.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a84dcda19adf4e49271709ba3cfe48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8d69c214ec6ae9233c7c2f21685177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4754574a3b4f416cae9e3251347907c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214d9a4f6648f9b37bb3bb9ee078c0b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4453ce4c6d461f1370048150f671497e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201195e69e7d74cf49a9ba32c8b2c3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201195e69e7d74cf49a9ba32c8b2c3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7db499662471ba1e6879d326104637d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65d545d67d024b7d19575df07bd4ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceee7288022589e3ee1c46f843321b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201195e69e7d74cf49a9ba32c8b2c3ab.png)
(2)求证:对于任意一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac19e2a797cd0a408316988a63b3755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ac76ff59a7ce5a47c563659ef4e80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
您最近一年使用:0次
4 . 已知
.在
中,
设
,
定义:
.
设
或
.给出下列四个结论:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3216c7108baab2601471b965ecb5694a.png)
②
;
③若
,则
;
④
,都有
,则
最多有
个元素.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edec660383c08c26ff438d1b8c7a3177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c852b101e577e4b7d3af668489b0ea5.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888390fce47b31855712344fd536bce1.png)
定义:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21090f6a3148c6c09a6946c4611fcd7.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2143cab296d997c652c495982e90cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddbe12fb60130709d275f169dc99c22.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3216c7108baab2601471b965ecb5694a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71daa66564dc886bd4c4f19d83396fd4.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616cdc04ccc5cae9cf8b941ebeb45ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0430ebe2730db038a644d8939a0d73.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9d43ee737b96bb2cd0cc241d6e1efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2509cacc1596557ea46e0f94e84823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
5 . 给定正整数
,任意的有序数组
,
,定义:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb7a18149d91f94f0df6809403f9ed.png)
(1)已知有序数组
,
,求
及
;
(2)定义:n行n列的数表A,共计
个位置,每个位置的数字都是0或1;任意两行都至少有一个同列的数字不同,并且有只有一个同列的数字都是1;每一行的1的个数都是a;称这样的数表A为‘
表’.
①求证:当
时,不存在‘
表’;
②求证:所有的‘
表’的任意一列有且只有a个1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ed67043f7ad15e42d9e92b58adf81c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfcca94c8524dfefe471fd55be83736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f00e0cc3c5765444157900fee292f7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb7a18149d91f94f0df6809403f9ed.png)
(1)已知有序数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3500e2bc7384abda0ca78edaec3f6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778b1b95b10df70df052e1e1ceaca2c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ac911432046e3e6c58c5c599d54216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468eb380831acf6234e8b8aac2267daa.png)
(2)定义:n行n列的数表A,共计
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1ef8b58951134267aea088bb1ca4c4.png)
①求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1ef8b58951134267aea088bb1ca4c4.png)
②求证:所有的‘
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1ef8b58951134267aea088bb1ca4c4.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
6 . 中国的农历七月初七被称为“七夕节”,象征着爱情与美好.某商场为了迎接“七夕节”的到来,特推出了购物抽奖活动.如图是由一个正方形与正三角形构成的图形,在点
处各安装了一盏灯,每次只有一处的灯亮起.初始状态是点
处的灯亮起,输入程序运行次数的上限
,然后按下开始按钮,程序开始运行,下一次是与
相邻点处的其中一盏灯随机亮起,再下一次是与上一次灯亮处相邻点的其中一盏灯随机亮起.若在运行过程中,点
处的灯再次亮起,则游戏结束,否则运行
次后游戏自动结束.在程序运行过程中,若点
处的灯再次亮起,则顾客获奖.现顾客小王参与抽奖活动.
,求小王获奖的概率.
(2)若
,记游戏结束时程序运行的次数为
,求
的分布列与期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d75df9d80ce1e0b7cb50464e293864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511d1fa76a49c3a367f87d5dfbe6091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
您最近一年使用:0次
7 . 若有穷自然数数列
:
满足如下两个性质,则称
为
数列:
①
,其中,
表示
,这
个数中最大的数;
②
,其中,
表示
,这
个数中最小的数.
(1)判断
:2,4,6,7,10是否为
数列,说明理由;
(2)若
:
是
数列,且
,
,
成等比数列,求
;
(3)证明:对任意
数列
:
,存在实数
,使得
.(
表示不超过
的最大整数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9092e6c4f9186b55324c3a43ecd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5fe1c847904911c89504cef0973214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1445aef0f66cacf3c0b358775623fab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b14e03f30c56d9943e4a82d0e029b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94beabf4bfbaa67081f1755fa5553a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e598a5ba40123abea0f6e4559535a61b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b14e03f30c56d9943e4a82d0e029b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daaf260a47403a2bdddd1268ebc44cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a878ab2590307a7a6f7afe576b7112c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1cb4ffc937e336200fd70fc089041a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](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/5da4cd81500bdb43118150dbdb1541e6.png)
(3)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9092e6c4f9186b55324c3a43ecd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e005b9c19a9b287aeefaa3af850beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
8 . 已知:
为有穷正整数数列,其最大项的值为
,且当
时,均有
.设
,对于
,定义
,其中,
表示数集M中最小的数.
(1)若
,写出
的值;
(2)若存在
满足:
,求
的最小值;
(3)当
时,证明:对所有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3665eb490a4be3b7b1a98238753899ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f927412b623486cde0d3f7d8aa8f264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6026d3efaa278220e3553d9802402bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2555a7889a95a7c4f8817340843c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb413e11e509aa1118694ad662785ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e934982c8340194b4396399b7f4b24bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d51777d3fca1ee8f588a6c39190dae.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1ae4b6456261b2948255780c39de17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c65edaa726a93d0600b7bb0a9bcc2ad.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb995c875a663dc8e907ba2d22ff7af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624bef0b515a06caf80cd3b7a3161aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb8b473e53c4f073f717eabe1d33f4.png)
您最近一年使用:0次
2024-04-09更新
|
1122次组卷
|
4卷引用:2024年北京高考数学真题平行卷(提升)
(已下线)2024年北京高考数学真题平行卷(提升)北京市海淀区2024届高三下学期期中练习(一模)数学试题2024届河北省雄安新区部分高中高考三模数学试题甘肃省白银市靖远县第一中学2024届高三下学期模拟预测数学试题
9 . 对正整数
,设数列
.
是
行
列的数阵,
表示
中第
行第
列的数,
,且
同时满足下列三个条件:①每行恰有三个1;②每列至少有一个1;③任意两行不相同.记集合
或
中元素的个数为
.
(1)若
,求
的值;
(2)若对任意
中都恰有
行满足第
列和第
列的数均为1.
①
能否满足
?说明理由;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3900a6f09149151f7d8479912e1a48e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1430ce165611dfc92e924a1cdc6c8220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223f93ed43c7772a367043ae224b75da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c734e1b65651e598e1a907a041664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51c223d60883c551607e8b6e8d7fd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2dce4d63752586495edc8d58dfc45bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cde6077954017c6ac884c0e76662c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224dcfa6dae1dc0511ad72da8617283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2c5e187752ef828b307951da554bb.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32708eeade6cbb36e1dfda113eececd0.png)
您最近一年使用:0次
10 . 设自然数
,由
个不同正整数
构成集合
,若集合
的每一个非空子集所含元素的和构成新的集合
,记
为集合
元素的个数
(1)已知集合
,集合
,分别求解
.
(2)对于集合
,若
取得最大值,则称该集合
为“极异集合”
①求
的最大值(无需证明).
②已知集合
是极异集合,记
求证:数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23747e7321187323c665a641adb49e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29fd31a1808968790032a671f64be90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29fd31a1808968790032a671f64be90.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccaf946a034215b8c49c12a1aff7790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d160c80e7542650f9ac8ff3981548ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11391d21b5da91adc137d57a73c19b83.png)
(2)对于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
②已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e9ca7e90d47d7ee295338bbac2d8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7477e3d7c54f409ee9905e81c9cbe2f.png)
您最近一年使用:0次