### Home > APCALC > Chapter 11 > Lesson 11.3.2 > Problem11-101

11-101.

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

1. $(−∞, ∞)$

1. $(−1, 1)$

1. $[−1, 1]$

1. $(−1, 1]$

1. $[−1, 1)$

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

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

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