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

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) $R = 1 , I = [ - 1,1 ]$