Question

Determine the radius of convergence of the series sum n=0 -> infinity for (x^n)/n!

Answer 1

it is infinity right

Answer 2

Using the ratio test, we get that
\[\lim_{n\to\infty} \left\vert \frac{x^{n+1}}{x^n} \cdot\frac{n!}{(n+1)!}\right\vert=\lim_{n\to\infty}\left\vert \frac{x}{n+1}\right\vert=0\]
So the series will converge for all values of x, you're right.