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

问题描述:

(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)
=(1/2)(3/2)(2/3)(4/3)……(8/9)(10/9)
中间约分
=(1/2)(10/9)
=5/9