The set 1/n (n = 1,2,...) doesn't contain any limit points (can you see why?), but it certainly has a limit point (can you see what the limit point is?) and so from the definition we see that this set is not closed.
The solution is presumably judicious applications of conditional expectations and properties of Brownian motion. It's certainly worth having a go yourself and if you don't mind me asking how far have you got? As a (rather unhelpful) hint your first move is the reason x doesn't turn up in the...