New sequence and inequalities associated with the Euler-Mascheroni constant using the sum of inverse odd natural numbers

Résumé

Using the classical sequence that converges to the Euler-Mascheroni constant, we will define a new sequence and new inequalities associated with the Euler-Mascheroni constant using the sum of inverses numbers of odd natural numbers. As a consequence we establish an estimate for the sum of inverses of odd natural numbers.