(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)
=3/2*4/3*……*101/100*1/2*2*3*……*99/100
=101/2*1/100
=101/200
(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)
=3/2*4/3*……*101/100*1/2*2*3*……*99/100
=101/2*1/100
=101/200