作业帮(1+1/2)*(1-1/2)*(1+1/3)(1-1/3).(1+1/99)*(1-1/99)
来源：学生作业帮助网 编辑：作业帮 时间：2024/06/21 03:11:25
(1+1/2)*(1-1/2)*(1+1/3)(1-1/3).(1+1/99)*(1-1/99)
(1+1/2)*(1-1/2)*(1+1/3)(1-1/3).(1+1/99)*(1-1/99)
(1+1/2)*(1-1/2)*(1+1/3)(1-1/3).(1+1/99)*(1-1/99)
(1+1/2)*(1-1/2)*(1+1/3)(1-1/3).(1+1/99)*(1-1/99)
=3/2*1/2*4/3*2/3*……*100/99*98/99
=1/2*100/99
=50/99
= (1-1/2)(1+1/2)(1-1/3)(1+1/3)......(1-1/99)(1+1/99)
=(1/2)(3/2)(2/3)(4/3)......(98/99)(100/99)
=(1/2)[(3/2)(2/3)][(4/3)(3/4)......[(99/98)(98/99)](100/99)
=(1/2)(100/99)
=50/99
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原式＝3/2*1/2*4/3*2/3*5/4*3/4*6/5*4/5*7/6*5/6*……*100/99*98/99
＝1/2*100/99
＝50/99