SCHWEITZER 1962 Problem 8

Denote by $M(r,f)$ the maximum modulus on the circle $|z|=r$ of the transcendent entire function $f(z)$ , and by $M_n(r,f)$ that of the $nth$ partial sum of the power series of $f(z)$ . Prove that the existence of an entire function $f_0(z)$ and a corresponding sequence of positive numbers $r_1<r_2<...\rightarrow +\infty$ such that $$\limsup_{n\rightarrow\infty} \frac{M_n(r_n,f_0)}{M(r_n,f_0)}=+\infty$$ [P. Turan]