(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*......*(1+1/99)*(1-1/99)=(1-(1/2)^2)(1-(1/3)^2)*......*(1-(1/99))^2=(1-1/4)(1-1/9)(1-1/16)*......*(1-1/9801)=(3/4)*(8/9)*(15/16)*......*(9800/9801)=2*2*......
