Let M={(x,y)∈R×R:x2+y2≤r2}, where r>0. Consider the geometric progression an=12n−1,n=1,2,3,… . Let S0=0 and, for n≥1, let Sn denote the sum of the first n terms of this progression. For n≥1 let Cn denote the circle with center (Sn−1,0) and radius an and Dn denote the circle with center (Sn−1,Sn−1) and radius an.Consider M with r=(2199−1)√22198. The number of all those circles Dn that are inside M is

Let M={(x,y)∈R×R:x2+y2≤r2}, where r>0. Consider the geometric pro

1.	Let M={(x,y)∈R×R:x2+y2≤r2}, where r>0. Consider the geometric progression an=12n−1,n=1,2,3,… . Let S0=0 and, for n≥1, let Sn denote the sum of the first n terms of this progression. For n≥1 let Cn denote the circle with center (Sn−1,0) and radius an and Dn denote the circle with center (Sn−1,Sn−1) and radius an.Consider M with r=(2199−1)√22198. The number of all those circles Dn that are inside M is
Answer» Let $M = {(x, y) \in R \times R : x^{2} + y^{2} \leq r^{2}}$ , where $r > 0$ . Consider the geometric progression $a_{n} = \frac{1}{2^{n - 1}}, n = 1, 2, 3, \dots .$ 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 $(S_{n - 1}, 0)$ and radius $a_{n}$ and $D_{n}$ denote the circle with center $(S_{n - 1}, S_{n - 1})$ and radius $a_{n}$ . Consider $M$ with $r = \frac{(2^{199} - 1) \sqrt{2}}{2^{198}}$ . The number of all those circles $D_{n}$ that are inside $M$ is