要从1/2,1/3,1/4,1/5,.1/49,1/50这49个数中挑出7不同个分数,使他们的和为1,求这7个分数.

题目

要从1/2,1/3,1/4,1/5,.1/49,1/50这49个数中挑出7不同个分数,使他们的和为1,求这7个分数.

答案

1/2+1/6=2/3
1/2+1/6+1/12=3/4
1/2+1/6+1/12+1/20=4/5
1/2+1/6+1/12+1/20+1/30=5/6
1/2+1/6+1/12+1/20+1/30+1/42=6/7
1/2+1/6+1/12+1/20+1/30+1/42+1/7=1