(1-1/2^2)(1-1/3)(1-1/4^2)…(1-1/9^2)*(1/10^2)

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 16:24:38

(1-1/2^2)*(1-1/3)*(1-1/4^2)*…*(1-1/9^2)*(1/10^2)
(1-1/2^2)*(1-1/3)*(1-1/4^2)*…*(1-1/9^2)*(1/10^2)

(1-1/2^2)*(1-1/3)*(1-1/4^2)*…*(1-1/9^2)*(1/10^2)
(1-1/2^2)*(1-1/3)*(1-1/4^2)*…*(1-1/9^2)*(1/10^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.*(1-1/9)(1+1/9)(1-1/10)(1+1/10)
=1/2*3/2*2/3*4/3*3/4*5/4*.*8/9*10/9*9/10*11/10
=1/2*11/10
=11/20