I’ve been meaning to submit this to the Proofs Without Words column ever since I discovered it way back when I was learning calculus. At the time, I wasn’t very impressed by showing that the harmonic series diverged using integral approximations for some reason. I wish I could remember why — it would probably make me a better calculus teacher. This is what I came up with to show the divergence more directly(?):
I’ll leave the interpretation as a puzzle to the reader.