1/42+1/56+1/72+1/90+1/110+1/132=?

1/42+1/56+1/72+1/90+1/110+1/132=?
1/42+1/56+1/72+1/90+1/110+1/132=?

1/42+1/56+1/72+1/90+1/110+1/132=?
1/42+1/56+1/72+1/90+1/110+1/132=?
=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12
=1/6-1/12
=1/12

1/42+1/56+1/72+1/90+1/110+1/132
=1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)+1/(10*11)+1/(11*12)
=(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+(1/10-1/11)+(1/11-1/12) (中间项正负相消了)
=1/6-1/12
=1/12
规律：1/(a*b)=[1/(b-a)]*(1/a-1/b)