Finding the Taylor series expansion of $f(z)=\frac{e^{z}-1}{z}$ around $0$ 
Find the Taylor series expansion of $f(z)=\displaystyle\frac{e^{z}-1}{z}$ around $0$.

I have no idea where to start.

Hint: Do you know how to find the taylor series expansion of $e^z$ around zero? Let $e^z=\sum_{n=0}^\infty a_nz^n$. Then $$f(z)=(e^z-1)/z=(\sum_{n=0}^\infty a_nz^n-1)/z$$
