Find the Radius of Convergence Of $\sum _ { n = 0 } ^ { \infty } \frac { ( - 3 ) ^ { n } ( x - 1 ) ^ { n } } { \sqrt { n + 1 } }$

question 216

Multiple Choice

Find the radius of convergence of $\sum _ { n = 0 } ^ { \infty } \frac { ( - 3 ) ^ { n } ( x - 1 ) ^ { n } } { \sqrt { n + 1 } }$ .

• A) \(\left( \frac { 2 } { 3 } , \frac { 4 } { 3 } \right]\)
• B) \(\left[ \frac { 2 } { 3 } , \frac { 4 } { 3 } \right)\)
• C) \(\left( \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)\)
• D) \(\left[ \frac { 1 } { 2 } , \frac { 3 } { 2 } \right]\)
• E) \(( 0,2 ]\)
• F) \([ 0,2 )\)
• G) \(( - 1,3 )\)
• H) \([ - 2,4 ]\)

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