CPM Homework Help : APCALC Problem 11-101

Multiple Choice: The interval of convergence for the series $\displaystyle \sum _ { n = 1 } ^ { \infty } \frac { ( x - 1 ) ^ { n } } { n ! }$ is:

Step 1:

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

Step 2:

$\lim \limits_{n\to\infty}\frac{|x-1|}{n+1}$

Step 3:

$= 0$
What does this tell you about the interval of convergence?