doi:10.1186/s13660-017-1507-8engAdell, J.A.Lekuona, A.Monotone and fast computation of Euler’s constantART-2017-104712We construct sequences of finite sums (l˜n)n=0 and (u˜n)n=0 converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant ¿ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product representation for 2 ¿ converging in a monotone and fast way at the same time. We use a probabilistic approach based on a differentiation formula for the gamma process.2017http://zaguan.unizar.es/record/6970010.1186/s13660-017-1507-8http://zaguan.unizar.es/record/69700oai:zaguan.unizar.es:69700info:eu-repo/grantAgreement/ES/DGA/E64info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67006-PJOURNAL OF INEQUALITIES AND APPLICATIONS 2017 (2017), 224 [9 pp]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess