(1/2003-1)(1/2002-1)(1/2001-1)...*(1/1001-1)(1/1000-1)

(1/2003-1)(1/2002-1)(1/2001-1)...*(1/1001-1)(1/1000-1)
(1/2003-1)(1/2002-1)(1/2001-1)...*(1/1001-1)(1/1000-1)

(1/2003-1)(1/2002-1)(1/2001-1)...*(1/1001-1)(1/1000-1)
1/2003-1=-2002/2003
1/2002-1=-2001/2002
1/2001-1=-2000/2001
...
1/1001-1=-1000/1001
1/1000-1=-999/1000
因为共有2003-1000+1=1004个负数相乘,所以结果为正
得：
2002/2003×2001/2002×2000/2001×……×1000/1001×999/1000
=999/2003

(1/2003-1)(1/2002-1)(1/2001-1)...*(1/1001-1)(1/1000-1)
=2002/2003*2001/2002*2000/2001*....*1000/1001*999/1000
=999/2003