莱布尼兹三角形问题

````````````````1/1`````````````1/2``` 1/2`````````1/3``` 1/6``` 1/3``````1/4` `1/12` `1/12`` 1/4````1/5 1/20 ``1/30 ``1/20` 1/5``1/6 1/30 `1/60 `1/60 `1/30` 1/61/7 1/42 1/105 1/140 1/105 1/42 1/7 把数阵依金字塔式整齐写好 就可以发现两边的数的既定的,第n行第1个数就是a(n,1)=1/n 然后依次往内填充 在中线以左的数a(n,m)是由a(n-1,m-1)-a(n,m-1)计算出 所以a(10,3)=a(9,2)-a(10,2) =[a(8,1)-a(9,1)]-[a(9,1)-a(10,1)] =1/8-1/9-1/9+1/10 =1/360