Originally Posted by

**DemonGal711** I have to determine whether the sequence converges or diverges and, if it does converge, find the limit. I'm confused about these two.

arctan(2x)

The limit of arctan(x) as x goes to infinity is pi/2. So, doesn't arctan(2x) do the same, just the behavior around the origin is altered? Can I just put that the limit of arctan(2x) is pi/2 even if I really didn't do anything to prove it?

__ln x __

ln 2x

Both go to infinity, the denominator goes just a bit quicker. So, I do l'hopital rule and I get

__1/x __

2/2x

1/x * 2x/2

Which reduces to 1 if I'm not mistaken. So, I get the obvious limit.

lim 1 = 1

which means my original problem's limit is 1. Is that right? It just seemed to easy to me.