(1-1/2^2)(1-1/3^2)...(1-1/2000^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/2000)(1+1/2000)
=1/2*2001/2000
=2001/4000