I am attending a course in calculus and need to find the supremum and infimum of the set $A$.
$$A := \left\{2(-1)^{n+1} + (-1)^{\frac12(n(n+1))} \left(2 + \frac 3n\right): n \in \Bbb N\right\}$$
I am puzzled as to how to treat this set. I tried computing the limit for $n \to 1$ and $n\to\infty$; with poor success.