Find the Radius of Convergence and the Interval of Convergence $$\sum _ { n = 1 } ^ { \infty } \frac { 3 \cdot 6 \cdot 9 \cdot \cdots \cdot 3 n } { 4 \cdot 7 \cdot 10 \cdots \cdot ( 3 n + 1 ) } x ^ { 2 n + 1 }$$

question 99

Multiple Choice

Find the radius of convergence and the interval of convergence of the power series. ]
Select the correct answer.
$$\sum _ { n = 1 } ^ { \infty } \frac { 3 \cdot 6 \cdot 9 \cdot \cdots \cdot 3 n } { 4 \cdot 7 \cdot 10 \cdots \cdot ( 3 n + 1 ) } x ^ { 2 n + 1 }$$

• A) \(R = \infty , I = ( - \infty , \infty )\)
• B) \(R = 1 , I = ( - 1,1 )\)
• C) \(R = 0 , I = \{ 0 \}\)
• D) \(R = 1 , I = [ - 1,1 ]\)

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