6. As shown in Figure 2, a circle is inscribed in a square with side length 2, another square is inscribed in this circle, and then another circle is inscribed in the second square. This process continues. If $S_{n}$ represents the total area of the first $n$ circles, then $\lim S_{n}=(\quad)$.
(A) $2 \pi$
(B) $\frac{3}{2} \pi$
(C) $\frac{4}{3} \pi$
(D) $\pi$