Resumen: We 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. Idioma: Inglés DOI: 10.1186/s13660-017-1507-8 Año: 2017 Publicado en: JOURNAL OF INEQUALITIES AND APPLICATIONS 2017 (2017), 224 [9 pp] ISSN: 1025-5834 Factor impacto JCR: 0.966 (2017) Categ. JCR: MATHEMATICS rank: 79 / 309 = 0.256 (2017) - Q2 - T1 Categ. JCR: MATHEMATICS, APPLIED rank: 130 / 252 = 0.516 (2017) - Q3 - T2 Factor impacto SCIMAGO: 0.546 - Applied Mathematics (Q2) - Discrete Mathematics and Combinatorics (Q3) - Analysis (Q3)