你是不是分子分母打反了
1/30=1/(5*6)=1/5-1/6
1/42=1/(6*7)=1/6-1/7
1/56=1/(7*8)=1/7-1/8
1/72=1/(8*9)=1/8-1/9
所以1/30+1/42+1/56+1/72
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/5-1/9=(9-5)/45=4/45