1 . 杨辉是我国南宋时期数学家,在其所著的《详解九章算法》一书中,辑录了图①所示的三角形数表,这比欧洲早500多年.杨辉三角本身包含很多性质,并有广泛的应用.借助图②所示的杨辉三角,可以得到,从第0行到第
行:第1斜列之和
;第2斜列之和
.类比以上结论,并解决如下问题:图③所示为一个
层三角垛,底层是每边堆
个圆球的三角形(底层堆积方式如图所示),向上逐层每边少1个,顶层是1个.则小球总数______ .
![](https://img.xkw.com/dksih/QBM/2023/7/6/3274809585278976/3277234630230016/STEM/1fbeb283409b4aae9dcf5027e2700387.png?resizew=533)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac0e2b2036ef092891ca0982b84b070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90d397c728bfb4f5334e3493aad4781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae0b861522b18be1753acc4474cbc9f.png)
![](https://img.xkw.com/dksih/QBM/2023/7/6/3274809585278976/3277234630230016/STEM/1fbeb283409b4aae9dcf5027e2700387.png?resizew=533)
![](https://img.xkw.com/dksih/QBM/2023/7/6/3274809585278976/3277234630230016/STEM/f0ff0aac26644cc89140bbf84617b91c.png?resizew=119)
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2023-07-09更新
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3卷引用:四川省资阳市2022-2023学年高二下学期期末数学理科试题