For a natural number $n$, point $\mathrm { A } _ { n }$ is on the $x$-axis. Point $\mathrm { A } _ { n + 1 }$ is determined according to the following rule. (가) The coordinates of point $\mathrm { A } _ { 1 }$ are $( 2,0 )$. (나) (1) Let $\mathrm { P } _ { n }$ be the point where the line passing through point $\mathrm { A } _ { n }$ and parallel to the $y$-axis meets the curve $y = \frac { 1 } { x } ( x > 0 )$. (2) Let $\mathrm { Q } _ { n }$ be the point obtained by reflecting $\mathrm { P } _ { n }$ about the line $y = x$. (3) Let $\mathrm { R } _ { n }$ be the point where the line passing through $\mathrm { Q } _ { n }$ and parallel to the $y$-axis meets the $x$-axis.
For a natural number $n$, point $\mathrm { A } _ { n }$ is on the $x$-axis. Point $\mathrm { A } _ { n + 1 }$ is determined according to the following rule.\\
(가) The coordinates of point $\mathrm { A } _ { 1 }$ are $( 2,0 )$.\\
(나) (1) Let $\mathrm { P } _ { n }$ be the point where the line passing through point $\mathrm { A } _ { n }$ and parallel to the $y$-axis meets the curve $y = \frac { 1 } { x } ( x > 0 )$.\\
(2) Let $\mathrm { Q } _ { n }$ be the point obtained by reflecting $\mathrm { P } _ { n }$ about the line $y = x$.\\
(3) Let $\mathrm { R } _ { n }$ be the point where the line passing through $\mathrm { Q } _ { n }$ and parallel to the $y$-axis meets the $x$-axis.