Wrong limit?

Questions
,
1

Hello! I am a student trying to understand why this limit [lim n->+infinity (nsen(n)+n^2)/(n^(1/3)+tan^-1((n^2)/(n+1)))] gives me no result on wolfram while it seems to me that the result is plus infinity.
I thought that there is a strange calculation about the function of the tan^-1 which I can’t explain.

2

Probably unable to interpret “nsen(n)”.

3

Should "nsen(n) be the product of n and the sine of n? If so – and using correct Wolfram language syntax:

    Limit[(n Sin[n] + n^2)/(n^(1/3) + ArcTan[n^2/(n + 1)]), 
     n -> \[Infinity]]
(* \[Infinity] *)
4

Limit.png
Limit.png791×601 23.1 KB

I copied the correction and this is the limit I’m looking for, though I don’t know why the result isn’t infinity.

5

Version 12.0 of Mathematica seems to be fine with this.

Limit[(n*Sin[n] + n^2)/(n^(1/3) + ArcTan[n^2/(n + 1)]), n → Infinity]

(* Out[1]= [Infinity] *)

Offhand I have no idea why W|A is faltering.