Confirming that the sequence $a_n = \frac{\sqrt{n}\cos{n}}{\sqrt{n^3}-1}$ converges I'm still trying to totally grasp the differences in proofs for sequences and series. I have a sequence $a_n = \frac{\sqrt{n}\cos{n}}{\sqrt{n^3}-1}$
In order to prove that this sequence converges, would it be correct to state that since:
$ -1 \le \cos{n} \le 1$ ,
and for $n \to \infty$ , $\sqrt{n^3}-1 \gt \sqrt{n}$
The denominator will be increasingly larger than the numerator therefore the sequence converges?

You can write
\begin{equation}
-\frac{\sqrt{n}}{\sqrt{n^3}-1}\le\frac{\sqrt{n}\cos{n}}{\sqrt{n^3}-1}\le\frac{\sqrt{n}}{\sqrt{n^3}-1}
\end{equation}
and you use the squeeze theorem.
