## anonymous 5 years ago Determine the radius of convergence of the series sum n=0 -> infinity for (x^n)/n!

1. anonymous

it is infinity right

2. anonymous

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.