古希腊毕达哥拉斯派的数学家研究过各种多边形数,如三角形数1,3,6,10,…,第
个三角形数为
,记第
个
边形数为
,以下列出了部分
边形数中第
个数的表达式:
三角形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0952b61bbfdaa6b247a5ef3fb710a6e8.png)
正方形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05edb4a9219fc13cf95fd385a42ddec.png)
五边形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ad5b0c9ed691250c1746077dc27f5.png)
六边形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4387d337cf3b99f2fcbff40a4e0889eb.png)
…
可以推测
的表达式,由此计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5436e4e410e1e58d2006ac7952071f.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed99d7d1f2f95cbf505da0e1a855864a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e106fd93948acb89af84f966468f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
三角形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0952b61bbfdaa6b247a5ef3fb710a6e8.png)
正方形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05edb4a9219fc13cf95fd385a42ddec.png)
五边形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ad5b0c9ed691250c1746077dc27f5.png)
六边形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4387d337cf3b99f2fcbff40a4e0889eb.png)
…
可以推测
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3636c99eb5312627e7e235236d51b28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5436e4e410e1e58d2006ac7952071f.png)
更新时间:2016-12-04 09:03:48
|
相似题推荐
填空题-单空题
|
适中
(0.65)
【推荐1】传说古希腊毕达哥拉斯学派的数学家经常在沙滩上面画点或用小石子表示数.他们研究过如图所示的三角形数:
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122493845504/1572122499514368/STEM/1b93702c9758403ebc351373aa1d3da9.png?resizew=215)
将三角形数1,3,6,10, 记为数列{an},将可被5整除的三角形数按从小到大的顺序组成一个新数列{bn},可以推测:(Ⅰ)
是数列
中的第__________ 项;(Ⅱ)
=__________ .(用n表示)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122493845504/1572122499514368/STEM/1b93702c9758403ebc351373aa1d3da9.png?resizew=215)
将三角形数1,3,6,10, 记为数列{an},将可被5整除的三角形数按从小到大的顺序组成一个新数列{bn},可以推测:(Ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f3ca3ddaa96376983d4da0e91c8d278.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122493845504/1572122499514368/STEM/9104ff6bea3c4b46b045f8268972a2c6.png?resizew=31)
您最近一年使用:0次
填空题-单空题
|
适中
(0.65)
名校
【推荐2】观察下列各式:
则
的末四位数字为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291019e73d72dbd5451974b159412a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c813c9064138cc7ae4eaffee73a4f1.png)
您最近一年使用:0次