Nicola Oresmo demonstrates the divergence of the harmonic series (1/1 + 1/2 + 1/3 + 1/4 + …) in an elementary way: he points out that the sum of the inverses of 3 and 4, as well as of 5, 6, 7, 8, as well as of 9, 10, 11, 12, 13, 14 and so on, is always at least equal to 1/2, and the series of 1/2 diverges by Archimedes’ principle.
