Question

括号里的二的平方分之一乘括号里的一减三的平方分之一一直这样然后到十... 怎么写

教教 别错了

Answer 1

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

Answer 2

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

Answer 3

=1/4*8/9*15/16*24/25*---------*99/100=11/60
属于有限树,无简便法