English: A smoothed version of the divergent series 1 + 2 + 3 + 4 + ⋯. This diagram is analogous to Sum1234Plain.svg, but a smoothing function
has been applied, so that the blue curve is the graph of the function
.
The horizontal scale has also been compressed so that the asymptotic growth of the function is x2/2, to aid comparison with the original series.
The blue curve asymptotically approaches the parabola , which is depicted in the companion diagram Sum1234Asymptote.svg.
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