Find the least upper bounds and the greatest lower bound of $A_2$ = {$\frac{n-1}{n+1}$ $\frac{cos 2n\pi}{3}$ :$ n\in \mathbb{N}$}

Question

Find the least upper bounds and the greatest lower bound of $A = \left\{\frac{n-1}{n+1} \cos\left(\frac{ 2n\pi}{3}\right) \mid n\in \mathbb{N}\right\}$

My Trial : i take $n= 1$ , here i get $A =0$ , for $n=2$, $A= \frac{1}{4}$,,,,,,,,

Now im confused how can i find the the least upper bounds and the greatest lower bound of $A$.

Any Hints/ solution will be appreciated

Thanks in advance