Find the Radius of Convergence and the Interval of Convergence $\sum _ { n = 0 } ^ { \infty } \left( \frac { n x } { 6 } \right) ^ { n }$

question 139

Multiple Choice

Find the radius of convergence and the interval of convergence of the power series. $\sum _ { n = 0 } ^ { \infty } \left( \frac { n x } { 6 } \right) ^ { n }$

• A) \(R = 0 , I = \{ 0 \}\)
• B) \(R = \infty , I = ( - \infty , \infty )\)
• C) \(R = 6 , I = [ - 6,6 ]\)
• D) \(R = 6 , I = ( - 6,6 )\)

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