Let zn = Arg(-1 + i/n). Find limn→∞ zn
Definition of convergence of a sequence.
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?