The Taylor series for a function (at least I presume you are talking about a single variable function) to N + 1 terms about a point x = a has the form:

or in summation notation:

For the error estimate I will refer you here as I have forgotten which one is "standard" (if any.)

So as an example, let and let us expand the series about the point .

We have:

So the Taylor series to 4 terms looks like:

-Dan