Question

quick question about series. if i have the closed form of a series, does the derivative of the series equal the derivative of the closed form? ill type out a specific example

Answer 1

\[\sum_{n=0}^{\inf}\frac{z^n }{ n! } = e^z\]

Answer 2

does the derivative of \[\sum_{n=0}^{\inf} \frac{ z^n }{ n! } \]
equal the derivative of e^z?

Answer 3

so if g(z) = the original summation, then g(z) would be equal to e^z. would this imply that g'(z) would be the derivative of e^z?