两千多年前,古埃及人总喜欢把分数转化为分子是1的分数来计算,所以后人常把分子是1的分数称为埃及分数.埃及分数在计算中有着一些什么规律呢?请观察下面几组算式并填空: (1) 1 3 - 1 4 = (4)-(3) 3×4 = 1 3×4 1 7 - 1 8 = ()-() 7×8 = 1 7×8 1 20 - 1 21 = ()-() 20×21 = 1 20×21 1 100 - 1 101 = () () … 1 a - 1 a+1 = a+1 a?a+1 - 1 a?(a+1) = 1 a?(a+1) (2)请你根据上面的规律,把下面各个分数写成两个分数的差. 1 2×3 = 1 () - 1 () 1 5×6 = 1 () - 1 () 1 40×41 = 1 () - 1 () 1 1999×2000 = 1 () - 1 () 1 42 = 1 () - 1 () 1 9900 = 1 () - 1 () 1 72 = 1 () - 1 () 1 n?(n+1) = 1 () - 1 () .