English: The divergent series 1 + 2 + 3 + 4 + ⋯. The first few partial sums of the series are 1, 3, 6, and 10, which appear as the height of the first few stair-steps. The terms 1, 2, 3, 4, and a corner of the term 5 are shown in alternating gray and yellow, to emphasize their individual contributions to the partial sums. The green parabola is the asymptote of the smoothed sum. Its y-intercept is -1/12, which is the regularized sum of the series