1 . 在探究
的展开式的二项式系数性质时,我们把二项式系数写成一张表,借助它发现二项式系数的一些规律,我们称这个表为杨辉三角(如图1),小明在学完杨辉三角之后进行类比探究,将
的展开式按x的升幂排列,将各项系数列表如下(如图2):
表示,即
展开式中
的系数为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9216a0f9d6e65ea4937ab7bf102c5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affdb56951c1eb5c394817b973cf4434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b87d2924395caf206ff6e6692c3cd0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affdb56951c1eb5c394817b973cf4434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdf138124aba5204739cafbf1b59d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83651456ad892247ebda19d98c40e9c.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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2卷引用:山东省泰安市2023-2024学年高二下学期期中考试数学试题
解题方法
2 . 若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47be4a899cfd2ec1e45d94f384a3b68.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:安徽省滁州市定远县育才学校2022-2023学年高二下学期期中数学试题
3 . 已知
(
且
,
).
(1)设
,求
中含
项的系数;
(2)化简:
;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dacd62755047aa73baeb8025df122be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31be670d32e753012125c503f2f3be56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22803ceb04e55261b8416f7c823864b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4382b9c757f0157f0938959edd4901.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3322f0b4d3bea41d30f8ac2fc0a750fd.png)
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2019-04-29更新
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4卷引用:【校级联考】江苏省无锡市江阴四校2018-2019学年高二下学期期中考试数学(理)试题
4 . 在集合
中,任取
个元素构成集合
. 若
的所有元素之和为偶数,则称
为
的偶子集,其个数记为
;若
的所有元素之和为奇数,则称
为
的奇子集,其个数记为
. 令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16947e41d7649b1d20694748dccdcd2.png)
(1)当
时,求
的值;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106cab7a8bb699ad77c92857deefc142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffa5fb6a7406201146f7b8d3343792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d20fd487c74eec4c5bdc1a830da427d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6552c3a42c2629ef9533f0fc651736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16947e41d7649b1d20694748dccdcd2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d228ae30f05bcb5ae4433c04a619e5e7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b41a9653d8b2c55e8dca3b987e4e51.png)
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3卷引用:江苏省南通市海安市海安高级中学2018-2019学年高二下学期06月月考数学试题