### Home > APCALC > Chapter 11 > Lesson 11.3.1 > Problem11-88

11-88.

Multiple Choice: The radius of convergence of $\displaystyle \sum _ { n = 1 } ^ { \infty } n ! x ^ { n }$ is: Homework Help ✎

1. $−1$

1. $0$

1. $\frac { 1 } { 2 }$

1. $1$

1. $\sqrt { 2 }$

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

$=\lim_{n\to\infty}(n+1)|x|$

$=\infty$

Therefore this series diverges for all $x$.