In continuation to my previous post : Inequality in Complex Plane I'm still having a small problem with a similar inequality :
For $z$ such that: $|z|> 1$ I wish to prove:
$1+|z|+\dots+|z^{n-1}| < \frac{|z^n|}{|z|-1}$
This reminds me of $\frac{1}{1-z} = 1+z+z^2+\dots$ but this is true only for $z$ such that $|z| < 1$ so I'm not sure what to do.