一又二分之一-六分之五+十二分之七-二十分之九+三十分之十一-四十二分之十三

一又二分之一-六分之五+十二分之七-二十分之九+三十分之十一-四十二分之十三
=(1+2)/(1×2)-(2+3)/(2×3)+(3+4)/(3×4)-(4+5)/(4×5)+(5+6)/(5×6)-(6+7)/(6×7)
=(1+1/2)-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)
=(1+1/2+1/3+1/4+1/5+1/6)-(1/2+1/3+1/4+1/5+1/6+1/7)
=1-1/7
=6/7

3/2 - 5/6 + 7/12 -9/20 +11/30 -13/42
= (1+1/2) -(1/2+1/3) +(1/3+1/4) -(1/4+1/5) +(1/5+1/6) -(1/6+1/7)
= 1-1/7
=6/7

一又二分之一-六分之五+十二分之七-二十分之九+三十分之十一-四十二分之十三
(3/2)-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)
解，得：
==[1+(1/2)]-[(1/2)+(1/3)]+[(1/3)+(1/4)]-[(1/4)+(1/5)]+[(1/5)+(1/6)]-[(1/6)+(1/7)]
==1-(1/7)
==6/7