Generally, you can make a conjecture about the upper bound of the sequence (try looking at it like a regular function and taking the limit). For example, you can guess that $ A(n) \rightarrow 3 $ as $ n \rightarrow \infty $. Then you must show, by definition of the upper bound of a sequence, that
$ \forall\epsilon>0 $, $ \exists s(\epsilon)\in A(n): inf[A(n)]-s(\epsilon)<\epsilon$
,where $ inf[A(n)] $ is the upper bound. Does that make intuitive sense? If you take $ \epsilon $ to be given, it will help you to draw a picture on the number line to see exactly what you're looking for. As a further hint, it will help you to know that there is an Archimedean property that says $ \forall\epsilon\in\mathbb{R},\exists n\in\mathbb{N}:\frac{1}{n}<\epsilon $