1/1*2 = 1 - 1/2 , 1/2*3 = 1/2 - 1/3 , .,1/39*40 = 1/39 - 1/40,
因此原式=1 - 1/2 +1/2 - 1/3 + ... + 1/39 - 1/40 = 1 - 1/40 = 39/40