HOW TO ADD UP LIKE KARL GAUSS
If you want to add a whole series of consecutive numbers, the trick is to think of them in pairs: the first and the last, the second and the second last, the third and the third last and so on. For instance, if you want to add all the numbers from 1 to 100, then the pairs would be 1 and 100, 2 and 99, 3 and 98 and so on. Each of the pairs adds to 101. There are 50 pairs. So 50 x 101 (or 5050) is the answer to the problem of having to add all numbers from 1 to 100. Adding from 1 to one million is just as easy. There are 500000 pairs which each add to 1000001, so the answer is 500000500000.