Find the Values of X for Which the Series $\sum _ { n = 1 } ^ { \infty } ( 2 x ) ^ { n }$

Multiple Choice

Find the values of x for which the series $\sum _ { n = 1 } ^ { \infty } ( 2 x ) ^ { n }$ converges.

A) $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$
B) $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$
C) $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$
D) 0
E) (-1, 1)
F) $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$
G) (-2, 2)
H) $( - \infty , \infty )$