hey there..
i've try this question already...
i got radius of convergence, R = 1/8
at x = 1/8,
converges...
at x = -1/8
i don't how to do this one..
please help me..
$\displaystyle a_n=\frac{8^n}{n!}x^n$
$\displaystyle |\frac{a_{n+1}}{a_n}|=|\frac{8^{n+1}}{(n+1)!}x^{n+ 1}\cdot\frac{n!}{8^nx^n}|=\frac{8|x|}{n+1}$
Now, $\displaystyle \lim_{n\to\infty}\frac{8|x|}{n+1}=0<1$ $\displaystyle \forall{x}\in(-\infty,\infty)$.
Therefore, the series converges $\displaystyle \forall{x}$ by the ratio test.
This implies an infinte radius.