CPM Homework Help : APCALC Problem 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:

$[–3, 3]$

$(–3, 3]$

$[–1, 1]$

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

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

Step 1:

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

Step 2:

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