1 . 已知函数
,且
在
上的最小值为0.
(1)求实数
的取值范围;
(2)设函数
在区间
上的导函数为
,若
对任意实数
恒成立,则称函数
在区间
上具有性质
.
(i)求证:函数
在
上具有性质
;
(ii)记
,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55386df48bce6389f5ea9dd827b2600d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277a2bf55ddf8cf07f22b2128712e2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08653fc03ff2c4ccaf3ab8b18474ee17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(i)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9626dc41063c34f4243b5a637668b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88209b9c5c9503721afc5696b8943a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2f05512a14030b8a9cd9c118ed962f.png)
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2 . (1)已知各项均为正数的无穷数列
满足:对于
,都有
,
,求数列
的通项公式;
(2)已知各项均为正数的无穷数列
满足:对于
,都有
,其中
为常数.
①若
,
,记
,数列
的前
项和
满足
,求数列
的通项公式:
②记
,证明:数列
中存在小于1的项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea27f3bbd9ff6515c7d957889202c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ed1465c2469cd518a13802bf6044fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知各项均为正数的无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86bb4325524dcb935bfd167cab6fb09f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ed1465c2469cd518a13802bf6044fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66884efff7400f92b530d69d029778d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472b92ebc99baaa71adf06ce85df434c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/1a4c9e626304cd58d8a995a0e4813ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d3db5570a5ab31ff7468c0d64d0f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
名校
解题方法
3 . “熵”常用来判断系统中信息含量的多少,也用来判断概率分布中随机变量的不确定性大小,一般熵越大表示随机变量的不确定性越明显.定义:随机变量
对应取值
的概率为
,其单位为bit的熵为
,且
.(当
,规定
.)
(1)若抛掷一枚硬币1次,正面向上的概率为
,正面向上的次数为
,分别比较
与
时对应
的大小,并根据你的理解说明结论的实际含义;
(2)若拋掷一枚质地均匀 的硬币
次,设
表示正面向上的总次数,
表示第
次反面向上的次数(0或1).
表示正面向上
次且第
次反面向上
次的概率,如
时,
.对于两个离散的随机变量
,其单位为bit的联合熵记为
,且
.
(ⅰ)当
时,求
的值;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b23512db3961f941a63a3d8254afb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449a066c87681f1f006aef2faeeba4c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c94a17b49550283be4ec1a348c8534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c84b931f584765cd30253af0e0d71b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1dc00bf0db4bf56d99cf9583938bcba.png)
(1)若抛掷一枚硬币1次,正面向上的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109ac38599926de9fd89470f561f6664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4479d54b1eced7c425e2deaefb18c233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6c6ec3ea184362694ba9c2dd2cbfd0.png)
(2)若拋掷一枚
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5470e9ee422d970529663964b84c45a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65362f7197f0e2cc05d879b3341584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0010cb466163db1349fc1040f6b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf395de82112cb78f446c6e7a245556a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8f9de90ca38f627eba375b15eb3e8f.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbabe5b63ff142225e3ae59e7b88b3c.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1109931e8c85ff6b8bb894e6d5d4017.png)
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2024-05-13更新
|
1221次组卷
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2卷引用:江苏省南通、扬州、泰州七市2024届高三第三次调研测试数学试题
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解题方法
4 . 已知F为抛物线C:
的焦点,点A在C上,
.点P(0,-2),M,N是抛物线上不同两点,直线PM和直线PN的斜率分别为
,
.
(1)求C的方程;
(2)存在点Q,当直线MN经过点Q时,
恒成立,请求出满足条件的所有点Q的坐标;
(3)对于(2)中的一个点Q,当直线MN经过点Q时,|MN|存在最小值,试求出这个最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0757f840f08c56d5d688cf4c1c25267b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)求C的方程;
(2)存在点Q,当直线MN经过点Q时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bee3672710a87854a3ecd3e169ffec.png)
(3)对于(2)中的一个点Q,当直线MN经过点Q时,|MN|存在最小值,试求出这个最小值.
您最近一年使用:0次
2024-05-11更新
|
1115次组卷
|
3卷引用:江苏省苏锡常镇四市2024届高三教学情况调研(二)数学试题
名校
解题方法
5 . 已知数列
的前n项和为
.若对每一个
,有且仅有一个
,使得
,则称
为“X数列”.记
,
,称数列
为
的“余项数列”.
(1)若
的前四项依次为0,1,
,1,试判断
是否为“X数列”,并说明理由;
(2)若
,证明
为“X数列”,并求它的“余项数列”的通项公式;
(3)已知正项数列
为“X数列”,且
的“余项数列”为等差数列,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42dd37c118e64c46c7fc37e21081745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450706c32e58d9e6ad2f14aabf9e81ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d255ea8e125b603d6b640bdf4a804922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771ca8c38c8a1646c83481a1d2bcfdfa.png)
您最近一年使用:0次
2024-05-07更新
|
1444次组卷
|
4卷引用:江苏省南京市2024届高三第二次模拟考试数学试题
江苏省南京市2024届高三第二次模拟考试数学试题(已下线)专题14 学科素养与综合问题(解答题19)黑龙江省牡丹江市第三高级中学2024届高三下学期第四次模拟数学试卷湖北省襄阳市第五中学2024届高三下学期第四次适应性测试数学试题
6 . 如图,
是边长为2的正方形纸片,沿某动直线
为折痕将正方形在其下方的部分向上翻折,使得每次翻折后点
都落在边
上,记为
;折痕
与
交于点
,点
满足关系式
.以点
为坐标原点建立坐标系,若曲线
是由点
的轨迹及其关于边
对称的曲线组成的,等腰梯形
的
分别与曲线
切于点P、Q、
,且
在x轴上.则梯形
的面积最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828edf1530dce9c69d2e844b2bf4a81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d659f763d2d33a685ba69df210dc1935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e849e0ace8c1ca612978a716d15cc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
A.6 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
7 . 在平面直角坐标系xOy中,已知椭圆Γ:
的离心率为
,直线l与Γ相切,与圆O:
相交于A,B两点.当l垂直于x轴时,
.
(1)求Γ的方程;
(2)对于给定的点集M,N,若M中的每个点在N中都存在距离最小的点,且所有最小距离的最大值存在,则记此最大值为
.
(ⅰ)若M,N分别为线段AB与圆O上任意一点,P为圆O上一点,当
的面积最大时,求
;
(ⅱ)若
,
均存在,记两者中的较大者为
.已知
,
,
均存在,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42aaceb687ffc763bdc5af3463c051a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631586067d81160678c2ddea983e62de.png)
(1)求Γ的方程;
(2)对于给定的点集M,N,若M中的每个点在N中都存在距离最小的点,且所有最小距离的最大值存在,则记此最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
(ⅰ)若M,N分别为线段AB与圆O上任意一点,P为圆O上一点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8207405e0cca2ccbd7643671bee4e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a34aca6d603ad0587bd4e3f1a0b01d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad8c255f18185a9b643c70edf9b00b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89815ff222757cbfc9b0ae2bf096a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed107042c263ccf28435954b8a02082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e99cb8baa4733c0d58735590ddaf51.png)
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2024-03-21更新
|
2764次组卷
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10卷引用:江苏省南通市2024届高三第二次调研测试数学试题
江苏省南通市2024届高三第二次调研测试数学试题江苏省扬州市2024届高三第二次调研测试数学试题江苏省泰州市2024届高三第二次调研测试数学试题(已下线)模块4 二模重组卷 第2套 全真模拟卷(已下线)江苏省南通市2024届高三第二次调研测试数学试题变式题 16-19(已下线)江苏省泰州市2024届高三第二次调研测试数学试题变式题16-19天津市南开中学2023-2024学年高三下学期第五次月考数学试题(已下线)高三数学考前押题卷3(已下线)专题8 考前押题大猜想36-40(已下线)压轴题02圆锥曲线压轴题17题型汇总-3
名校
解题方法
8 . 设集合
,其中
.若对任意的向量
,存在向量
,使得
,则称A是“T集”.
(1)设
,判断M,N是否为“T集”.若不是,请说明理由;
(2)已知A是“T集”.
(i)若A中的元素由小到大排列成等差数列,求A;
(ii)若
(c为常数),求有穷数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642ae5a0ccf07cc09fb140685e5fa2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247dbdb60e5215115103ba8e33a10611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bdf7f57b61c21324e21d25941135270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4483cc4e4c07bda4b90f4550b40b0ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2bf51f13526eb5b6f6732236bbe772.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab2da56e4587a8f90af2fe37f958f1f.png)
(2)已知A是“T集”.
(i)若A中的元素由小到大排列成等差数列,求A;
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c9df01c8fb5139e8a90d4d68cb8df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d02a8555da4dbbc7820a50a95b071ee.png)
您最近一年使用:0次
2024-03-20更新
|
980次组卷
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3卷引用:江苏省南通市海安高级中学2024届高三下学期开学考试数学试题
名校
解题方法
9 . 三阶行列式是解决复杂代数运算的算法,其运算法则如下:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c685c6a79c8293c8b5083c3a8dc4c.png)
若
,则称
为空间向量
与
的叉乘,其中
,
,
为单位正交基底. 以
为坐标原点、分别以
,
,
的方向为
轴、
轴、
轴的正方向建立空间直角坐标系,已知
,
是空间直角坐标系中异于
的不同两点
(1)①若
,
,求
;
②证明
.
(2)记
的面积为
,证明:
.
(3)证明:
的几何意义表示以
为底面、
为高的三棱锥体积的
倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c685c6a79c8293c8b5083c3a8dc4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e91aaddb8691f8afa477a96bf630631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aba64ae92194bc4f0f6e49725471542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8643f24c3af715421ec0ccd3224ed453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d541143135cb9b8166bc631a85ac6a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a471332d4f3731d90f62fdf819f39824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73db31aecdde14e0002f082d9091df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2980a18e4d0a2a795b7983a1a1866db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1821c677712026f8de34fe924b1f52a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41ef077626c88964805a45849471a1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb22d1c614d99e2639864e43f4b6277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00db2bada2cfc90c5213aca8af17df4c.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb8623a42db5ceb745a16d72739f513.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0505ce82dd5726c22fcaac54d01d630b.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8191a760981f2d67648905665c8b167a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad58b362528b814739ceb7fe5febfc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
您最近一年使用:0次
2024-03-07更新
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888次组卷
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8卷引用:江苏省扬州市仪征中学2024届高三下学期期初调研测试数学试题
江苏省扬州市仪征中学2024届高三下学期期初调研测试数学试题河南省部分重点高中2024届高三普通高等学校招生全国统一考试(期末联考)数学试卷 河南省部分重点高中(青桐鸣)2023-2024学年高三上学期期末大联考数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)江苏省江都中学2023-2024学年高二下学期3月联考数学试卷江苏省盱眙中学2023-2024学年高二下学期第一次学情调研数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点2 平面法向量求法及其应用(二)【培优版】(已下线)专题08 期末必刷解答题专题训练的7种常考题型归类-期末真题分类汇编(北师大版2019必修第二册)
10 . 国际象棋是国际通行的智力竞技运动.国际象棋使用
格黑白方格相间棋盘,骨牌为每格与棋盘的方格大小相同的
格灰色方格.若某种黑白相间棋盘与骨牌满足以下三点:①每块骨牌覆盖棋盘的相邻两格;②棋盘上每一格都被骨牌覆盖;③没有两块骨牌覆盖同一格,则称骨牌构成了棋盘的一种完全覆盖.显然,我们能够举例说明
格黑白方格相间棋盘能被骨牌完全覆盖.
格黑白方格相间棋盘的对角两格,余下棋盘不能被骨牌完全覆盖;
(2)请你切掉
格的黑白方格相间棋盘的任意两个异色方格,然后画出余下棋盘的一种骨牌完全覆盖方式,并证明:无论切掉的是哪两个异色方格,余下棋盘都能被骨牌完全覆盖;
(3)记
格黑白方格相间棋盘的骨牌完全覆盖方式数为
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb79f6535ee15a3d41ca71cf72082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(2)请你切掉
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5d94e748101eaf9aa5ae725b0040e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485596f7fc2aa8d80466a7d02a00af15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cfd722654be25b48b28ba0f6698e89.png)
您最近一年使用:0次
2024-03-06更新
|
785次组卷
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4卷引用:江苏省苏州大学2024届高考新题型2月指导卷数学试题
江苏省苏州大学2024届高考新题型2月指导卷数学试题山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题(已下线)第四套 最新模拟重组卷(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总