Converge or Diverge: arctan((n^3)/(n^2+6))

[Sir Andus]

The problem I've been having is whether or not this sequence converges or diverges. I'm not even really sure how to start this problem.

arctan((n^3)/(n^2+6))

I've been sitting on this problem for nearly an hour with no progress.

 

[stapel]

As n tends toward infinity, what does n³ / (n² + 6) tend toward? (Simplify this rational expression using long division, if necessary.)

Once you know what the argument of the arctangent tends toward, it should be immediately obvious what the limit value is. :wink:

Eliz.

 

[Sir Andus]

Thanks, it all makes sense now. I wasn't even looking at the problem that way. For some reason, I thought I needed to somehow had to get rid of arctan altogether using a derivative or integral. Silly me. Anyways, thanks.