Cute. To illustrate the sum of limits, however, I prefer a graphic with sum -> 1. Take an empty circle then add a chunk of shaded semicircle, then add one quarter, then add one eighth... you get the idea.
With this method you won't be able to tell converging sequences from diverging ones. Suppose I used your circle and put in the first hundred terms of the harmonic sequence (divided by 10 or so, to fit in the unit area).