Find the interval of convergence of the power series. (Be sure to include a check for convergence at the end points of the interval.) $$\sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { n } } { ( 4 n ) ! }$$
A) $\left[ \frac { - 1 } { 3 } , \frac { 1 } { 3 } \right)$
B) $[ - 1,1 )$
C) $( - 1,1 )$
D) $( - \infty , \infty )$
E) $( - 3,3 )$

Question

Quizplus · Accepted Answer

The series is a Maclaurin series for a function involving $e^{3x}$, which converges for all real numbers, hence the interval of convergence is $( - \infty , \infty )$.

Find the Interval of Convergence of the Power Series ∑n=0∞(3x)n(4n)!\sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { n } } { ( 4 n ) ! }n=0∑∞​(4n)!(3x)n​

Find the Interval of Convergence of the Power Series $\sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { n } } { ( 4 n ) ! }$