수학1_무한등비급수_난이도 중

무한수열 \(\{a_n\}\) 을 \[{a_n} = \left\{ {\begin{array}{ll}0\\1\\2\end{array}}\right.\;\;\;\;\begin{array}{ll}{\left( {n = 3k - 2} \right)}\\{\left( {n = 3k - 1} \right)}\\ {\left( {n = 3k} \right)}\end{array}\;\; (단, \; k는 \; 자연수)\]로 정의할 때 \(\sum \limits_{n=1}^{\infty} \dfrac{a_n}{4^n}\) 의 값은?

 

① \(\dfrac{3}{4}\)          ② \(\dfrac{2}{21}\)          ③ \(\dfrac{13}{32}\)          ④ \(\dfrac{17}{54}\)          ⑤ \(\dfrac{29}{63}\)

 

 

 

정답  ②