(1-1/2)(1-1/3)(1-1/4).(1-1/99)(1-1/100)等于?

(1-1/2)(1-1/3)(1-1/4).(1-1/99)(1-1/100)等于?
(1-1/2)(1-1/3)(1-1/4).(1-1/99)(1-1/100)等于?

(1-1/2)(1-1/3)(1-1/4).(1-1/99)(1-1/100)等于?
（1-1/2^2)*(1-1/3^)*(1-1/4^)*……*（1-1/99^2)*(1-1/100^2) =(1-1/2)(1+1/2)(1-1/3)(1+1/3)*.（1-1/99）(1+1/99)(1-1/100)(1+1/100)（平方差因式分解） =(1/2)*(3/2)(2/3)*(4/3)*.(98/99)*(100/99)(99/100)(101/100) =(1/2)*(101/100) =101/200请采纳回答,