## Calculus: Early Transcendentals 8th Edition

$R=5$ ; the interval of convergence is $(-5,5]$
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{x^{n+1}}{(n+1)5^{n+1}}}{\frac{x^n}{n5^ n}}|$ $=\frac{|x|}{5}$ Hence, $R=5$ ; the interval of convergence is $(-5,5]$