Recent content by szklany

Let (X,d) be a metric space, and x is an element in X. Show that \{y \in X|d(y,x)>r\} is open for all r in Reals. I really need some help with this one, I have almost no idea on how I am meant to solve this. The only thing i know is that I have to use the Openness definition, that states...

Find the sum of the infinite series \sum _{n=1}^{\infty } \left( i /2\right) ^{2\,n} I just can't seem to get started on this problem, so I was hoping somebody could give me a hint, as to what methods i should read up on.