1 . 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)
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2024-03-06更新
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802次组卷
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4卷引用: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
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 最新模拟重组卷江苏省苏州大学2024届高考新题型2月指导卷数学试题(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
名校
2 . 学习几何体结构素描是学习素描的重要一步.如图所示,这是一个用来练习几何体结构素描的石膏几何体,它是由一个圆柱
和一个正三棱锥
穿插而成的对称组合体.棱
和面
与圆柱侧而相切,点
是棱
与圆柱侧而的切点.直线
分别与面
,面
交于点
,圆柱
在面
,面
上分别截得椭圆
.在平面
和平面
中,椭圆
上分别有两组不重合的两点
和
(图中未画出).且满足关系
.已知三棱锥
的外接球表面积为
,圆柱的底面直径为
,请问平面
,平面
上是否分别存在点
,使得对于满足
的直线
分别恒过定点
.若存在,试求
和
夹角的余弦值:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8461e08e60b84222ef056f49e71fa20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad044057e3a5b2f033d9ad0006b6f50e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37d0645be8436fa5c7a6ee8ba7de527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357e0872d9e98d662a780e7686de86ee.png)
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![](https://img.xkw.com/dksih/QBM/2024/1/13/3410267677220864/3410816027746304/STEM/273256e47234495eaf4d1e8d41ba7a4a.png?resizew=183)
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