As far as i know it is related to Gauss. Write the sequences forward and backward first.
1 +2 +3 +.....+1002 1002+1001+1000+.....+1 --------------------------------------... Adding them 1003+1003+......(1002 times) =1002x1003 But this contains the series twice. So, the sum is = 1002x1003/2=501x1003=502503. answer
