(1-1/2^2)*(1-1/3^2)*.*(1-1/98^2)*(1-1/99^2)*(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)*.*(1-1/98)(1+1/98)(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3*.*97/98*99/98*98/99*100/99*99/100*101/100
=1/2*101/100
=101/200
(1-1/2^2)*(1-1/3^2)*.*(1-1/98^2)*(1-1/99^2)*(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)*.*(1-1/98)(1+1/98)(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3*.*97/98*99/98*98/99*100/99*99/100*101/100
=1/2*101/100
=101/200