Find the interval of convergence of the series.
-$$\sum _ { n = 1 } ^ { \infty } \frac { ( x - 4 ) ^ { n } } { ( 3 n ) ! }$$
A) $x \leq 5$
B) $3 \leq x \leq 5$
C) $- 2 \leq x \leq 10$
D) $- \infty

Question

Find the interval of convergence of the series.
-$$\sum _ { n = 1 } ^ { \infty } \frac { ( x - 4 ) ^ { n } } { ( 3 n ) ! }$$
A) $x \leq 5$
B) $3 \leq x \leq 5$
C) $- 2 \leq x \leq 10$
D) $- \infty < x < \infty$

Quizplus · Accepted Answer

The series is a power series centered at $x = 4$. The denominator grows extremely fast due to the factorial, which means the series converges for all $x$ (i.e., its radius of convergence is infinite).

Find the Interval of Convergence of the Series ∑n=1∞(x−4)n(3n)!\sum _ { n = 1 } ^ { \infty } \frac { ( x - 4 ) ^ { n } } { ( 3 n ) ! }n=1∑∞​(3n)!(x−4)n​

Find the Interval of Convergence of the Series $\sum _ { n = 1 } ^ { \infty } \frac { ( x - 4 ) ^ { n } } { ( 3 n ) ! }$