Proof by induction:

Mathematical Induction on degree of polynomial

Base case: Suppose the statement is true for n=1 case we prove it is true for n=2 case.

Induction step: We assume converges , for any polynomial of degree (k-1), We proceed to prove converges for apolynomial of degree k

is polynomial of degree (k-1) , by the assumption , we know converges there by also converges.

Hence, proved.