The starting term of the Maclaurin series

Question

I'm reading Brown & Churchill's Complex Variables and Applications. They define the Maclaurin series as $$f(z) = \sum_{n=0}^\infty\frac{f^{(n)}(0)}{n!} z^n, \text{ ($|z|<R_0$)},$$ where $R_0$ is the radius of convergence. But they say the Maclaurin series expansion of $e^z-1$ is $\sum_{n=1}^\infty \frac{z^n}{n!}$. $\sum_{n=1}^\infty \frac{z^n}{n!} \not = \sum_{n=0}^\infty \frac{z^n}{n!}$, isn't it? This is in Example 1 on page 215, 8th edition. The definition is given on page 190.

Answer 1

You almost have it:

$$e^z=\sum_{n=0}^\infty\frac{z^n}{n!}=1+\sum_{n=1}^\infty\frac{z^n}{n!}\implies e^z-1=\ldots$$