# What is an example of a Taylor Series?

Expand $f \left(x\right) = {e}^{x}$ at $0$.
${f}^{\left(n\right)} \left(x\right) = {e}^{x}$, so ${f}^{\left(n\right)} \left(0\right) = 1$.
e^x=1+x/1+x^2/(2!)+x^3/(3!)+x^4/(4!)+ * * *
$\frac{1}{1 - x} = 1 + x + {x}^{2} + {x}^{3} + {x}^{4} + \cdot \cdot \cdot$