I was trying to visualize the idea of convergence/divergence of series using complex plane. I got this idea from “A First Course in Complex Analysis with Applications by Dennis Zill, Patrick Shanahan”. I used the command:

`ComplexListPlot[Table[(0.9 I)^(n + 1)/n, {n, 1, 70, 0.01}],Joined -> True, PlotRange -> All, PlotStyle -> {Blue, Thick}] `

to generate a plot as shown below:

Alternatively, one can use the command

`ListLinePlot[Table[ReIm[(1.1 I)^(n + 1)/n], {n, 1, 70, 0.01}], PlotRange -> All] `

to generate the same. This series is convergent as it kind of spirals down. If we change 0.9i to 1.1i, the plot changes to

which signifies that the series is divergent. What is want is that some sort direction as to which way the sequence goes, like these:

How can this be achieved in mathematica?

Thanks in advance.