In the movie “All quiet on the Western front” from 1930 (which is an adaptation of the 1929 novel by Erich Maria Remarque), a scene where a soldier at the front mentions the sum of arithmetic series formula. The soldier says
S = A + N L/2
and finds it beautiful. How does this translate? The formula, as stated, has been crafted with a mathematician of taste. As the usual formula is messier, the short version gives the essential and provides the intuition of a rectangular area A plus the area n L/2 of a triangle.