(1-1/2^2)(1-1/3^2)(1-1/4^2)*.*(1-1/19^2)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.*(1-1/19)(1+1/19)=1/2*3/2*2/3*4/3*3/4*5/4*.*18/19*20/19=1/2*20/19=10/19