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

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- Aug 28th 2008, 04:18 PMbonselsmfind radius of convergence
find radius of convergence of sum(upper bound infinity and lower bound n=0) n!x^n

- Aug 28th 2008, 04:39 PMJhevon
by the ratio test, the radius of convergence will be given by the bounds of x such that

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

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

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