1-2-3+4+5-6-7+8+9-10-11+12+ ...+1997-1998-1999+2000
= (1-2-3+4)+(5-6-7+8)+(9-10-11+12)+ ...+(1997-1998-1999+2000)
= 0 + 0 + 0 + ...+ 0
= 0×500
= 0