(1-1/2^2)(1-1/3^2)(1-1/4^2)*.*(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.*(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3*3/4*5/4*.*99/100*101/100
=1/2*101/100
=101/200