Sum of 1, 2, 3, ... , n

The sum of a linear series is fairly easy to deduce. As seen below one writes down the series from 1 to n on the first row. The second row is the same series in reverse order. Adding each column separately one finds each sum is n+1. So twice the sum is n(n+1). Therefore, the sum is n(n+1)/2 as indicated in the last blog.