$\displaystyle \sum_{n=0}^{\infty}\frac{7^n}{n!}x^n$
I'm still trying to get the hang of these and feel like I've done something wrong here. After applying the ratio test I end up with:
$\left|7x\right|\lim \limits_{n \to \infty}\left|\frac{1}{n+1}\right|$
That limit is $0$, so does this mean my radius of convergence is $\infty$ and my interval of convergence is $(-\infty, \infty)$?