Hint: Add the first number to the last - does this help?
It's easiest to see that the first and last number are 1 and 1000, which add to 1001.
The next two numbers we can add are 2 and 999, which add to 1001.
The next two numbers to add are 3 and 998, which add to 1001.
We can keep doing this 500 times, and in each case they add to 1001.
And 500 x 1001 = 500,500.