2003*2002-2002*2001+2001*2000-2000*1999+.+3*2-2*1

2003*2002-2002*2001+2001*2000-2000*1999+.+3*2-2*1
=2002+2002^2-(2001+2001^2)+2000+2000^2-(1999+1999^2)+---+2+2^2-(1+1^2)
=(2002-2001+2000-1999+---+2-1)+(2002^2-2001^2+2000^2-1999^2+---+2^2-1)
=1001+(2002+2001)(2002-2001)+(2000+1999)(2000-1999)+--+(2+1)(2-1)
=1001+2002+2001+2000+1999+-----+2+1
=1001+(2002+1)*2002/2
=2006004