Identify the Interval of Convergence of a Power Series $\sum _ { n = 1 } ^ { \infty } n ( 2 x ) ^ { n }$

Multiple Choice

Identify the interval of convergence of a power series $\sum _ { n = 1 } ^ { \infty } n ( 2 x ) ^ { n }$

A) $- \frac { 1 } { 2 } < x < 0$
B) $- \frac { 1 } { 2 } < x < \frac { 1 } { 2 }$
C) $0 < x < \frac { 1 } { 2 }$
D) $- \frac { 1 } { 4 } < x < \frac { 1 } { 4 }$
E) $0 < x < \frac { 1 } { 4 }$