(1 - 1/4)(1 - 1/9)(1 - 1/16)...(1 - 1/100) =
= 3/4*8/9*15/16*24/25*35/36*48/49*63/64*80/81*99/100 =
= (3/9*8/4)(15/25*24/16)(35/49*48/36)(63/81*80/64)*99/100 =
= 2/3*3/5*3/2*5/7*4/3*7/9*5/4*99/100 =
= 3/7*4/3*7/9*5/4*(9*11)/100 = 4/9*5/4*(9*11)/100 = 11/20