Hi all I have this question from a lecture that I had earlier, the lecturer left the proof as an excercise. I asked him later in the week after a couple attempts and he said I should use proof by induction on n. I had another few cracks at it but I still haven't got anywhere with it. Any help would be very much appreciated. The question is:
"Let $f : R → R$ be a polynomial function of degree $n$ and let $a ∈ R$. Show that the $nth$ Taylor polynomial $P_{f,a,n}$ of $f$ at $a$ is equal to $f$, i.e. that $P_{f,a,n}(x) = f(x)$ for all $x ∈ R.$"