=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/2004)(1+1/2004)(1-1/2005)(1+1/2005)
=1/2 × 3/2 ×2/3 × 4/3 ×3/4 ×5/4 ×4/5 ×…… ×2005/2004×2004/2005 ×2006/2005
=1/2 ×2006/2005
=1003/2005