Find the radius of convergence and the interval of convergence of the power series. $\sum _ { n = 0 } ^ { \infty } \frac { ( 7 x ) ^ { n } } { n ! }$
A) $R = 7 , I = ( - 7,7 )$
B) $R = 0 , I = \{ 0 \}$
C) $R = 7 , I = [ - 7,7 ]$
D) $R = \infty , I = ( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The series is a Maclaurin series for $e^{7x}$, which converges for all x, hence the radius of convergence is $\infty$ and the interval of convergence is $(- \infty , \infty )$.

Find the Radius of Convergence and the Interval of Convergence ∑n=0∞(7x)nn!\sum _ { n = 0 } ^ { \infty } \frac { ( 7 x ) ^ { n } } { n ! }∑n=0∞​n!(7x)n​

Find the Radius of Convergence and the Interval of Convergence $\sum _ { n = 0 } ^ { \infty } \frac { ( 7 x ) ^ { n } } { n ! }$