# find radius of convergence

• August 28th 2008, 04:18 PM
bonselsm
find radius of convergence
find radius of convergence of sum(upper bound infinity and lower bound n=0) n!x^n
• August 28th 2008, 04:39 PM
Jhevon
Quote:

Originally Posted by bonselsm
find radius of convergence of sum(upper bound infinity and lower bound n=0) n!x^n

by the ratio test, the radius of convergence will be given by the bounds of x such that

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

be sure to check the end points. see post #2 here on how to do that

you may also want to check this out