CPM Homework Help : CALC Problem 12-12

Multiple Choice: The interval of convergence of the power series $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 3 ^ { n } x ^ { n } } { n ^ { 2 } }$ is:

$[ - 3,3 ]$

$( - 3,3 ]$

$[ - 1,1 ]$

$[ - \frac { 1 } { 3 } , \frac { 1 } { 3 } ]$

$( - \frac { 1 } { 3 } , \frac { 1 } { 3 } ]$

Hint:

$\lim\limits_{n\to\infty}\Bigg|\frac{\frac{3^{n+1}x^{n+1}}{(n+1)^2}}{\frac{3^nx^n}{n^2}}\Bigg|$