I am reviewing for a intro to complex class and am stumped by this question:
Suppose $f(z)$ is an entire function. We know $f'(n) = \frac{1}{n}$. Given $f(0) = 1$, find $f(2i)$.
Since $f$ is entire we can use a Maclaurin expansion. From the given info I know that $f'(0) = 0$ by continuity. I conjecture that $f^{(n)}(0) = 0$, for $n\geq 1$, but I don't know where to start to prove that.