I have problem with finding inf and sup of sets:
$$ A=\left\{ n\in N:\quad 2(-1)^{n+1}+(-1)^{n(n+1)/2} \left(2+\frac{3}{n}\right) \right\}$$
$$ B=\left\{ n\in N: \quad \frac{n-1}{n+1}\cos{\frac{2\pi n}{3}} \right\}$$
and solution in my textbook argue that sets $A,B$ can be rewritten as
$\displaystyle A = \{-3,-\frac{11}{2},5\} \cup \{\frac{3}{4k},-\frac{3}{4k+1},-4-\frac{3}{4k+2},4+\frac{3}{4k+3}\} $
$\displaystyle B = \{\frac{3k-1}{3k+1},-\frac{3k-2}{6k},-\frac{3k-3}{2(3k-1)}\}$ where $k \in N$
Could you explain me this transition? Because I don't get it