Show that $$\sum_{n=0}^{\infty}\frac{^n}{n!}$$ converges uniformly on the disk D = {z : |z| < r} for every r > 0. The series represents an analytic function S(z) on the entire complex plane. We know when z =x is real, $$S(x) = e^x$$
Anyone care to explain? I took the limit and it converges to 0 for all values of Z in the complex plane