We already know the constant series diverges if *a* ≠ 0. However, looking at the graph can help the intuition. Here's a 2-D graph of the constant series: Putting all the little rectangles together creates an infinitely long rectangle of height *a *> 0. The area of such a rectangle must be infinite. Since the sum of the constant series is the area of that rectangle, is infinite - in other words, the series diverges. At long last, we can give a proof that the harmonic series diverges (even though its terms converge to 0). |