试观察下列各式的规律,然后填空:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c97f3e0b3eb6ad36aaba9e6c3c6bbe9.png)
,
…
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd3d2d159fe49b184380e4b08f13518.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fc530917ade098f3a481f1ada4bd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c97f3e0b3eb6ad36aaba9e6c3c6bbe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfdc088d5384f01280e91e9b5964a40c.png)
…
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd3d2d159fe49b184380e4b08f13518.png)
更新时间:2024-03-15 19:23:00
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【知识点】 多项式乘法中的规律性问题解读
相似题推荐
填空题
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较易
(0.85)
【推荐1】教材
页《数学史话》谈到:我国南宋数学家杨辉所著的《详解九章算法》(
年)一书中,用如图的三角形解释二项式乘方展开式中相关系数的规律,法国数学家帕斯卡于
年才发现此三角形,比中国晚了几百年,杨辉在注释中提到,在他之前北宋数学家贾宪(
年左右)也用过这种方法,因此我们称这个三角形为“杨辉三角”或“贾宪三角”.此图揭示了
(n为非负整数)的展开式的项数及各项系数的有关规律:
(1)观察发现:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
________ ;
(2)
的展开式中所有项的系数和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbcf82603580ddba4cfdb4efde85a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9226d42c0e35c51c7118a27fd62b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1ea6275ee45d9ebd91d6377c7ca1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f758fcf0427957c498c592644e9369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9216a0f9d6e65ea4937ab7bf102c5db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/12/3e9b0d5b-bb76-4472-942e-6d565eff1831.jpg?resizew=345)
(1)观察发现:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621dac22799ee9ed6e1713f4fcfa6108.png)
您最近一年使用:0次
填空题
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【推荐2】我国南宋数学家杨辉所著的《详解九章算术》一书中,用下图的三角形解释二项式
的展开式的各项系数,此三角形称为“杨辉三角”.请看图(1),并观察下列等式(2):
![](https://img.xkw.com/dksih/QBM/2020/2/14/2398793968599040/2398967768285185/STEM/fc423a47-0275-4d85-8404-a3d50554b44f.png)
根据前面各式的规律,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc24c10307892c287fd03c1aaa64fb1d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5abcb3802cf02be93a8c89067bd49a.png)
![](https://img.xkw.com/dksih/QBM/2020/2/14/2398793968599040/2398967768285185/STEM/fc423a47-0275-4d85-8404-a3d50554b44f.png)
根据前面各式的规律,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc24c10307892c287fd03c1aaa64fb1d.png)
您最近一年使用:0次