State the Cauchy integral formula.

Assuming that the function $f(z)$ is analytic in the disc $|z|<1$, prove that, for every $0<r<1$, it is true that

$$\frac{d^{n} f(0)}{d z^{n}}=\frac{n !}{2 \pi i} \int_{|\xi|=r} \frac{f(\xi)}{\xi^{n+1}} d \xi, \quad n=0,1, \ldots$$

[Taylor's theorem may be used if clearly stated.]