1/42+1/56+1/72+1/90+1/110

1/42+1/56+1/72+1/90+1/110

1/6*7 + 1/7*8 + 1/8*9 +1/9*10 + 1/10*11
=1/6-1/7+1/7-1/8……1/10-1/11
=1/6-1/11
=5/66

1/72=1/(6*7)
1/56=1/(7*8)
1/72=1/(8*9
1/90=1/(9*10)
.....
原式=1/6-1/7+1/7-1/8+1/8-1/9+1/9- 1/10+1/10-1/11
=10/11

当然可以。拆分就行了。
1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11=5/66