### Home > APCALC > Chapter 12 > Lesson 12.1.1 > Problem12-13

12-13.

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

1. $[–3, 3]$

1. $(–3, 3]$

1. $[–1, 1]$

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

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

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

$=\lim\limits_{n\to\infty}3|x|<1$