(1-1/4)*(1-1/9*(1-1/16)*…*(1-1/2500)=?

问题描述:

(1-1/4)*(1-1/9*(1-1/16)*…*(1-1/2500)=?

(1-1/4)*(1-1/9*(1-1/16)*…*(1-1/2500)=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4).(1+1/50)(1-1/50)=1/2x3/2x2/3x4/3x3/4x5/4x...x49/50x51/50=1/2x51/50=51/100