Find the radius of convergence of $\sum _ { n = 1 } ^ { \infty } \frac { ( x + 2 ) ^ { n } } { n ^ { 2 } 3 ^ { n } }$ .
A)0
B)1
C)2
D)3
E)4
F)5
G)6
H) $\infty$

Question

Quizplus · Accepted Answer

The radius of convergence $ R $ can be found using the formula $ R = \frac{1}{\limsup_{n \to \infty} |a_n|^{1/n}} $, where $ a_n = \frac{1}{n^2 3^n} $. Here, $\limsup_{n \to \infty} |a_n|^{1/n} = \frac{1}{3}$, so $ R = 3 $.

Find the Radius of Convergence Of ∑n=1∞(x+2)nn23n\sum _ { n = 1 } ^ { \infty } \frac { ( x + 2 ) ^ { n } } { n ^ { 2 } 3 ^ { n } }∑n=1∞​n23n(x+2)n​

Find the Radius of Convergence Of $\sum _ { n = 1 } ^ { \infty } \frac { ( x + 2 ) ^ { n } } { n ^ { 2 } 3 ^ { n } }$