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06063006 Mortici, Cristinel Accurate bounds for a convergence to gamma constant. Sci. Stud. Res., Ser. Math. Inform. 20, No. 2, 49-54 (2010). 2010 Vasile Alecsandri University of Bac\u au, Facultyof Sciences, Bac\u au EN Euler-Mascheroni constant speed of convergence inequalities approximations Summary: The aim of this paper is to improve the result of {\it T. Negoi} [Gaz. Matem. Ser. A 15 111--113 (1997)] about the convergence speed of a sequence convergent to Euler-Mascheroni constant.