Notice that 1 + 999 = 1000, 3 + 997 = 1000, 5 + 995 = 1000, etc.

You have to figure out how many pairs there are in your sum. We can figure this out if we take 1-99 and then extrapolate. Since there are 100 number is 1-100, there would be 50 number in 1-100 odd; we're pairing 2 numbers of the 50, so we would have 25 pairs of numbers in 1-100. If we multiply that by 10 (because we're looking at 1-1000, not 1-100), we would have 2500 pairs of numbers that add up to 1000.