Question 100
For each positive integer $n$ consider the set $A_n$ of all the numbers obtained by choosing signs in $\pm 1 \pm 2 \pm \cdots \pm n$; for instance, $A_2 = \{-3, -1, 1, 3\}$ and $A_3 = \{-6, -4, -2, 0, 2, 4, 6\}$. Find the cardinal of the set $A_n$.