On the zeros of tails of power series

Let f(z)=∑k=0∞akzkf(z)=∑k=0∞akzk (1.1) be a power series with a positive radius of convergence. Let sn(z)=∑k=0nakzk,tn(z)=∑k=n+1∞akzksn(z)=∑k=0nakzk,tn(z)=∑k=n+1∞akzk be its nth section and nth tail, respectively.