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
Taylor series in \(\mathbb R\)
f(x)=\sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n
Geometric series
\dfrac{1}{1-z} = 1+ z + z^2 + z^3+ \cdots
Geometric series
\dfrac{1}{1-z} = 1+ z + z^2 + z^3+ \cdots
\dfrac{1}{1-z} = 1+ z + z^2 + z^3+ \cdots