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