原式=（1-1/2)(1+1/2)(1-1/3）（1+1/3)*(1-1/4)(1+1/4)*...*(1-1/2004)(1+1/2004)
=1/2*3/2*2/3*4/3*3/4*...*2003/2004*2005/2004
=1/2*2005/2004
=2005/4008