A new approach to solve the inverse equation of point kinetics is presented. The neutron density history can be considered as a series of infinite Bernoulli numbers. In order to simplify the problem, the proposed method uses an approximation which considers only two derivatives of the neutron population density. The reactivity is calculated for different forms of neutron population density and for different time steps. Due to its high precision, the results obtained suggest that the proposed method can be used in a real-time digital reactivity meter.