The sequence is $a_n = (-1)^n +2/n, \quad n =1,2,3,...$ and $A= \left\{a_n : n=1,2,3,...\right\}$. The questions are :
$i)$ to calculate the $\lim_{n \to \infty}$sup $ a_n$ and $\lim_{n \to \infty}$inf $ a_n$
$ii)$ Determine the limit points of A.
$iii)$ Is A open? Why?
$iv)$ Is A closed? Why?
$v)$ Has A any isolated points? If so which?
$vi)$Determine $\overline A$.
Appreciate your answers.