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

question 30

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) \(0 < x < \frac { 1 } { 4 }\)

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