For a natural number $n ( n \geqq 2 )$, let $a _ { n }$ and $b _ { n } \left( a _ { n } < b _ { n } \right)$ be the $x$-coordinates of the two distinct points where the line $y = - x + n$ and the curve $y = \left| \log _ { 2 } x \right|$ meet. Which of the following statements in are correct? [4 points] Remarks ㄱ. $a _ { 2 } < \frac { 1 } { 4 }$ ㄴ. $0 < \frac { a _ { n + 1 } } { a _ { n } } < 1$ ㄷ. $1 - \frac { \log _ { 2 } n } { n } < \frac { b _ { n } } { n } < 1$ (1) ᄀ (2) ᄂ (3) ᄃ (4) ᄂ, ᄃ (5) ᄀ, ᄂ, ᄃ
For a natural number $n ( n \geqq 2 )$, let $a _ { n }$ and $b _ { n } \left( a _ { n } < b _ { n } \right)$ be the $x$-coordinates of the two distinct points where the line $y = - x + n$ and the curve $y = \left| \log _ { 2 } x \right|$ meet. Which of the following statements in <Remarks> are correct? [4 points]
\textbf{Remarks}\\
ㄱ. $a _ { 2 } < \frac { 1 } { 4 }$\\
ㄴ. $0 < \frac { a _ { n + 1 } } { a _ { n } } < 1$\\
ㄷ. $1 - \frac { \log _ { 2 } n } { n } < \frac { b _ { n } } { n } < 1$\\
(1) ᄀ\\
(2) ᄂ\\
(3) ᄃ\\
(4) ᄂ, ᄃ\\
(5) ᄀ, ᄂ, ᄃ