Find the radius of convergence of $\sum _ { n = 0 } ^ { \infty } ( 3 x ) ^ { n }$ .
A)3
B)0
C)2
D) $\frac { 1 } { 6 }$
E)6
F) $\frac { 1 } { 3 }$
G)1

H) $\frac { 1 } { 2 }$

Question

Find the radius of convergence of $\sum _ { n = 0 } ^ { \infty } ( 3 x ) ^ { n }$ .
A)3
B)0
C)2
D) $\frac { 1 } { 6 }$ 
E)6
F) $\frac { 1 } { 3 }$ 
G)1

H) $\frac { 1 } { 2 }$

Quizplus · Accepted Answer

The radius of convergence for a power series $\sum _ { n = 0 } ^ { \infty } a_n x^n$ can be found using the formula $R = \frac{1}{\limsup_{n \to \infty} \sqrt[n]{|a_n|}}$. For the series $\sum _ { n = 0 } ^ { \infty } (3x)^n$, $a_n = 3^n$, so $R = \frac{1}{\limsup_{n \to \infty} \sqrt[n]{3^n}} = \frac{1}{3}$.

Find the Radius of Convergence Of ∑n=0∞(3x)n\sum _ { n = 0 } ^ { \infty } ( 3 x ) ^ { n }∑n=0∞​(3x)n

Find the Radius of Convergence Of $\sum _ { n = 0 } ^ { \infty } ( 3 x ) ^ { n }$