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