  Recent pioneering experiments on non-Markovian dynamics done e.g. for active
matter have demonstrated that our theoretical understanding of this challenging
yet hot topic is rather incomplete and there is a wealth of phenomena still
awaiting discovery. It is related to the fact that typically for simplification
the Markovian approximation is employed and as a consequence the memory is
neglected. Therefore methods allowing to study memory effects are extremely
valuable. We demonstrate that a non-Markovian system described by the
Generalized Langevin Equation (GLE) for a Brownian particle of mass $M$ can be
approximated by the memoryless Langevin equation in which the memory effects
are correctly reproduced solely via the effective mass $M^*$ of the Brownian
particle which is determined only by the form of the memory kernel. Our work
lays the foundation for an impactful approach which allows to readily study
memory-related corrections to Markovian dynamics.
