Let \(F(z)=\sum^{\infty}_{k=0}a_ kz^ k\) be a transcendental entire function and let c be an arbitrary complex number. Let \(p_ n(z)=\sum^{n}_{k=0}a_ kz^ k\). In this paper the author proves that if R is any nonnegative number, then there is a positive integer N such that \(p_ n(z)-c\) has a zero in \(| z| >R\) for all \(n>N\).