For an infinite geometric sequence $\left\{ a _ { n } \right\}$, choose all correct statements from \textless Remarks\textgreater. [3 points] \textless Remarks\textgreater ㄱ. If the infinite geometric series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ converges, then $\sum _ { n = 1 } ^ { \infty } a _ { 2 n }$ also converges. ㄴ. If the infinite geometric series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ diverges, then $\sum _ { n = 1 } ^ { \infty } a _ { 2 n }$ also diverges. ㄷ. If the infinite geometric series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ converges, then $\sum _ { n = 1 } ^ { \infty } \left( a _ { n } + \frac { 1 } { 2 } \right)$ also converges. (1) ㄱ (2) ㄴ (3) ㄱ, ㄷ (4) ㄱ, ㄴ (5) ㄴ, ㄷ
For an infinite geometric sequence $\left\{ a _ { n } \right\}$, choose all correct statements from \textless Remarks\textgreater. [3 points]
\textless Remarks\textgreater\\
ㄱ. If the infinite geometric series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ converges, then $\sum _ { n = 1 } ^ { \infty } a _ { 2 n }$ also converges.\\
ㄴ. If the infinite geometric series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ diverges, then $\sum _ { n = 1 } ^ { \infty } a _ { 2 n }$ also diverges.\\
ㄷ. If the infinite geometric series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ converges, then $\sum _ { n = 1 } ^ { \infty } \left( a _ { n } + \frac { 1 } { 2 } \right)$ also converges.\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄱ, ㄴ\\
(5) ㄴ, ㄷ