Question

What is an example of a Taylor Series?

Answer 1

Expand `f(x)=e^x` at `0`.

`f^((n))(x)=e^x`, so `f^((n))(0)=1`.

`e^x=1+x/1+x^2/(2!)+x^3/(3!)+x^4/(4!)+ * * *`

Or the geometric series:

`1/(1-x)=1+x+x^2+x^3+x^4+ * * *`