Find the Radius of Convergence and the Interval of Convergence $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } ( x - 6 ) ^ { n } } { n \cdot 5 ^ { n } }$

question 72

Multiple Choice

Find the radius of convergence and the interval of convergence of the power series. $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } ( x - 6 ) ^ { n } } { n \cdot 5 ^ { n } }$

• A) \(R = 6 , I = ( - 1,11 ]\)
• B) \(R = 5 , I = ( 1,11 ]\)
• C) \(R = \frac { 1 } { 5 } , I = \left[ - \frac { 1 } { 5 } , \frac { 1 } { 5 } \right)\)
• D) \(R = 5 , I = [ - 5,5 )\)

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The extent to which a study is free from systematic error or bias, allowing for the accurate attribution of causality to the variable being studied.

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