Taylor series in \(\mathbb C\)

f(z)=\displaystyle\sum_{n=0}^{\infty} a_n(z-z_0)^n,\;\; (|z-z_0|<R)

a_n=\frac{f^{(n)}(z_0)}{n!},\;\; (n=0,1,2,\ldots)

Taylor series in \(\mathbb R\)

f(x)=\displaystyle\sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n

f(x)=\sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n

\dfrac{1}{1-z} = 1+ z + z^2 + z^3+ \cdots

\dfrac{1}{1-z} = 1+ z + z^2 + z^3+ \cdots

By Juan Carlos Ponce Campuzano

Geometric representation of series