CPM Homework Help : APCALC Problem 11-60

For what values of $x$ does $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { x ^ { 2 n + 1 } } { n ! }$ converge?

Step 1:

Use the Ratio Test:

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

Step 2:

$\large\lim\limits_{n\to\infty}\Big|\frac{x^2}{n+1}\Big|=?$