Question

Let
M=\left\\{(x, y) \in R \times R: x^{2}+y^{2} \leq r^{2}\right\\},
where r$$>$$0. Consider the geometric progression $a_{n}=\frac{1}{2^{n-1}}, n=1,2,3, \ldots$ Let $S_{0}=0$ and for $n \geq 1$, let $S_{n}$ denote the sum of the first $n$ terms of this progression. For $n \geq 1$, let $C_{n}$ denote the circle with center $\left(S_{n-1}, 0\right)$ and radius $a_{n}$, and $D_{n}$ denote the circle with center $\left(S_{n-1}, S_{n-1}\right)$ and radius $a_{n}$.