(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*......*(1+1/99)*(1-1/99)=(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*......*(1-1/99)*(1+1/99)=1/2*3/2*2/3*4/3*.................*98/99*100/99=1/2*100/99=50/99