when he was in elementary school, his teacher once tried to keep the children busy, telling them to add up all the numbers from 1 to 100. gauss did it quickly, like this: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on. there were a total of 50 pairs, so 50 × 101 = 5,050. the formula is formula_1. according to this archived website, the problem given to gauss was actually more difficult to do.