I have this problem I'm working on. Hints are much appreciated (I don't want complete proof):
In a normed vector space, if $ x_n \longrightarrow x $ then $ z_n = \frac{x_1 + \dots +x_n}{n} \longrightarrow x $
I've been trying adding and subtracting inside the norm... but I don't seem to get anywhere.
Thanks!