2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212118We consider a random walk on integers where at the first visits to a site the walker gets a positive drift, but where after a certain number of visits the walker gets a negative drift. We prove that the walker is almost surely transient to the left with positive speed.As noticed by a referee, the result of this note follows from a recent result of Kosygina and Zerner (simply by using a monotonicity argument)Probability60F05; 60F20text