你会算出下面埃及分数的和吗?试试看.

拆项相加:
(1-1/2)+(1/2-1/3)+(1/3-1/4)+........+(1/97-1/98)+(1/98-1/99)+(1/99-1/100)=1-1/100=99/100
不难呵

1/2 = 1/1*2 = 1/1 - 1/2
1/6 = 1/2*3 = 1/2 - 1/3
1/12 = 1/3*4 = 1/3 - 1/4
...
1/9900 = 1/99*100 = 1/99 -1/100

2分之1 6分之1 12分之1 20分之1 30分之1 ........... 9900分之1=
1/1 - 1/2 1/2 - 1/3 1/3 - 1/4 ... 1/99 -1/100 = 99/100

原式=1-1/2+1/2-1/3+…＋1/99-1/100
=1-1/100
=99/100