(1-1/2)(1+1/2)(1-1/3)(1+1/3)…(1-1/9)(1+1/9).

来源：学生作业帮助网编辑：六六作业网时间：2024/12/27 04:27:09

(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*…*(1-1/9)*(1+1/9).(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*…*(1-1/9)*(1+1/9).

(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*…*(1-1/9)*(1+1/9).
(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*…*(1-1/9)*(1+1/9).

(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*…*(1-1/9)*(1+1/9).
(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*…*(1-1/9)*(1+1/9)
=[(1-1/2)*(1-1/3)* ...*(1-1/9)]*[(1+1/2)*(1+1/3)* ...*(1+1/9)]
=[(1/2)*(2/3)*(3/4)*...*(8/9)]*[(3/2)*(4/3)*(5/4)*...*(10/9)]
=[1/9]*[10/2]=5/9

=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)……(8/9)(10/9)
=(1/2)*(10/9) 【中间的都约分约掉了】
=5/9

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/9)(1+1/9)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)……(8/9)(10/9)
中间的都约分约掉了
=(1/2)*(10/9)
=5/9