prove that a closed ball in Euclidean space is perfect

I've just been working with just the complex numbers z less than or equal to 1, but am curious as to how one would prove this for all closed balls in Rn as well. I only have up to Rudin page $33$ in my toolkit right now.

I already proved they are closed for my example, but I can't think of an argument to show that every point is a limit point.