Question 38187
Gauss showed the shortcut for this hundreds of years ago, when he was but a child...
Notice that if you add the first and last terms you get 4002.
If you add the second and second-to-last terms you get 4002.
If you add the third and third-to-last terms you get 4002.
And so on, and so on...
Now how many pairs making 4002's are there?
Well, half the number of numbers present.
There are 2000 even numbers from 2 to 4000.
That means 1000 pairs, each adding to 4002.
So the sum is 1000 * 4002 = 4002000.
Cool!