(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:2024/07/04 05:18:17
![(1-1/2^2)*(1-1/3)*(1-1/4^2)*…*(1-1/9^2)*(1/10^2)](/uploads/image/z/2754525-21-5.jpg?t=%281-1%2F2%5E2%29%2A%281-1%2F3%29%2A%281-1%2F4%5E2%29%2A%E2%80%A6%2A%281-1%2F9%5E2%29%2A%281%2F10%5E2%29)
(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