The Taylor series of a polynomial is the polynomial itself!!
You can still write the summation and possibly verify this of course.
Actually, no it isn't quite the same.Originally Posted by TD!
The Taylor series for a function f(x) about a point x = c is:
The notation is meant to represent the nth derivative of f evaluated at x = c. This form is only correct, of course, assuming the series converges for a given f(x) and c.
In this case your function is going to be:
I see what you mean, but the 'form' doesn't matter since the functions (the original result and the simplification to g(x) again) are completely the same.
I don't really see the use of this question, unless its intention is that the student sees that the taylor series of a polynomial is the polynomial again; by experimentally finding this through the formula like you did.