1. The problem statement, all variables and given/known data Let zn = Arg(-1 + i/n). Find limn→∞ zn 2. Relevant equations Definition of convergence of a sequence. 3. The attempt at a solution Well zn = Arg(-1 + i/n) = arctan(-1/n). So it seems clear that limn→∞arctan(-1/n) = arctan(limn→∞ -1/n) = arctan(0) = [itex]\pi[/itex]. Which is true if arctan is continuous. There's the problem, I don't know how to prove that arctan is continuous. It seems way more difficult that I expected. I can't seem to get anywhere with it. How do you show it? Or can anyone think of another way to find the limit?