(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/9)(1+1/9)(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3*3/4*……8/9*10/9*9/10*11/10
=1/2*11/10
=11/20