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

E)3
F)1
G) $\frac { 1 } { 3 }$

Question

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

E)3
F)1
G) $\frac { 1 } { 3 }$

Quizplus · Accepted Answer

The given series is a geometric series with a common ratio of $3x$. The radius of convergence $R$ for a geometric series is found using the formula $|r| < 1$, where $r$ is the common ratio. Here, $|3x| < 1$, which implies $|x| < \frac{1}{3}$. Therefore, the radius of convergence $R$ is $1$.

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

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