## Linear Operator Problem

Let $a~[0], ... , a~[n]$ be real numbers such that $a~[0]$ is nonzero, and let $L$ be the following linear operator: $a~[n]D^n + ... + a~[1]D + a~[0]I$.

Let $p(t)$ be a polynomial. Let us define the functions $y~[0] = p(t)$. and: $y~[k+1] = p(t) - (a~[n]D^n + ... + a~[1]D)[y~[k]]$.

Prove that the functions $y~[k](t)$ converge to a polynomial $y(t)$, and that $L[y] = p(t)$