写过程(1/2004-1) (1/2003-1) (1/2002-1)...(1/1001-1) (1/1000-1)=

一共有：2004-1000+1 = 1005 项
(1/2004-1)(1/2003-1)(1/2002-1)……(1/1001-1)(1/1000-1)
= (-2003/2004)(-2002/2003)(-2001/2002)……(-1000/1001)(-999/1000)
= - ( 2003 * 2002 * 2001*……*1001*1000*999) / (2004 * 2003 * 2002*2001*……*1001*1000)
= - (1/2004) (2003/2003)(2002/2002)(2001/2001)……(1001/1001)(1000/1000)(999/1)
= - (1/2004)(999)
= - 999/2004