Resumen: We present a new simple proof of Euler’s formulas for Z(2k), where k= 1,2,3,.... The computation is done using only the defining properties of the Bernoulli polynomials and summing a telescoping series, and the same method also yields integral formulas for Z(2k+ 1). Idioma: Inglés DOI: 10.4169/amer.math.monthly.122.5.444 Año: 2015 Publicado en: American Mathematical Monthly 122, 5 (2015), 444-451 ISSN: 0002-9890 Factor impacto JCR: 0.349 (2015) Categ. JCR: MATHEMATICS rank: 273 / 312 = 0.875 (2015) - Q4 - T3 Factor impacto SCIMAGO: 0.408 - Mathematics (miscellaneous) (Q3)