The first three of an infinite sequence, $P_n,$ of squares is drawn below:

The base of each square lies on the $x$ axis, and the upper-left vertex of each square lies on the line $y=\frac{x}{2}.$

You are given that $x_1=2.$

1. Show that $x_{n+1}=\frac{2}{3}{x}_n$. Find $x_2$ and $x_3$ and give an explicit formula, in terms of $n,$ for $x_n.$

2. Find the sum of the areas of the infinitely many squares $P_1,P_2,\dots$