I just installed Mathematica on a Raspberry Pi and I am playing around and I run into this. If I do the graph up to 34, I see discrete steps. Over 35, I start to see a mix of discrete steps and continuous line. This case below, with the graph going from 1 to 50 is a good example. Why is the line changing from steps to continuous, back to steps and back to continuous? changes the 50 to 34 and it looks only steps.
There are not enough PlotPoints. Try
PlotPoints
Plot[Sum[i, {i, 1, n}], {n, 1, 50}, PlotPoints -> 100]
or
ListStepPlot[Table[Sum[i, {i, 1, n}], {n, 1, 50}]]
