(2010-1)+(2000-2)+(1999-3)+.+(1002-1000)

(2010-1)+(2000-2)+(1999-3)+.+(1002-1000)

Original formula = (1001 + 1002 + 1003 +. + 2000) - (1 + 2 + 3 +. + 1000) + (2010-1001)
=(1001-1)+(1002-2)+.+(2000-1000)+(2010-1001)
=1000*1000+1009
=1001009