请回答我:(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*.*(1+1/99)*(1-1/99)的答案是多少?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/15 01:29:05

请回答我:(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*.*(1+1/99)*(1-1/99)的答案是多少?
请回答我:(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*.*(1+1/99)*(1-1/99)的答案是多少?

请回答我:(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*.*(1+1/99)*(1-1/99)的答案是多少?
(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*.*(1+1/99)(1-1/99)
=(1+1/2)(1+1/3)...(1+1/99)(1-1/2)(1-1/3)...(1-1/99)
=[3/2*4/3...100/99]*[1/2*2/3...98/99]
=100/2*1/99
=50/99

(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*......*(1+1/99)*(1-1/99)
=(1+1/2)*(1/1+3)*……*(1+1/99)*(1-1/2)*(1-1/3)*……*(1-1/99)
=(3/2*4/3*5/4*……*99/98*100/99)*(1/2*2/3*3/4*……*97/98*98/99)
=1/2*100*1/99
=50/99