I am having a problem with this question. Can someone help me please.
We are defining a sequence of polynomials such that:
$P_0(x)=1; P_n'(x)=nP_{n-1}(x) \mbox{ and} \int_{0}^1P_n(x)dx=0$
I need to prove, by induction, that $P_n(x)$ is a polynomial in $x$ of degree $n$, the term of highest degree being $x^n$.
Thank you in advance