Why $0$ is the accumulation point of the set $\Omega=\{\frac{1}{n}+\frac{i^n}{n} \mid n\in N / \{0\} \}$ ??
I try to solve it graphing the set $\Omega$ and I saw that the real part of the set when $n$ goes to $0$ it tends to infinity, then there is an indeterminate. The point $z_0$ is an accumulation point of $S$ if each deleted neighborhood of $z_0$ contains at least one point of $S$
Then give any $\epsilon >0$, I want to show that there exists one point in $\Omega$ other than $z=0$. In fact there exist an infinite numbers of points such that
$$\left|\frac{1}{n}+\frac{i^n}{n}\right|<\epsilon$$
If I choose $n$ to be even and positive and $n >\frac{1}{\epsilon}$, then $|\frac{1}{n}+\frac{i^n}{n}|<\epsilon$. Therefore, for any $\epsilon$, $N(1;\epsilon)$ contains at least one point in $\Omega$ other than $z=0$. Is my procedure correct??
