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We obtain two sequences of rational numbers which converge to theEuler-Gompertz constant. Denote by <f(x)> the integral of f(x)e^{-x} from 0 toinfinity. Recall that the Euler-Gompertz constant \delta is <ln(x+1)>.  Main idea. Let P_n(x) be a polynomial with integer coefficients. It is easyto prove that <P_n(x)ln(x+1)>=a_n+<ln(x+1)>b_n$ for some integers a_n, b_n.Hence if <P_n(x)ln(x+1)>/b_n converges to zero, a_n/b_n converges to - \delta .  Main Theorem. Let u be positive real. There exists polynomials P_n(x)(theyare explicitly given in the paper) such that <P_n(x)ln(xu+1)> tends to u as ntends to infinity.  Proof of Main Theorem is elementary.

Rational approximants for the Euler-Gompertz constant