Original: Gauss 's presumed method was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums : 1 + 100 = 101 , 2 + 99 = 101 , 3 + 98 = 101 , and so on , for a total sum of 50 Ã -- 101 = 5050 .
Simplified: 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 Ã -- 101 = 5,050 .