Visualizing convergence/divergence series

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:

enter image description here

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

enter image description here

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

enter image description here enter image description here

How can this be achieved in mathematica?

Thanks in advance.