On some sequences whose limit is the Euler gamma constant

Abstract

There are two known sequences of real numbers converging to the Euler gamma constant, one of them strictly decreasingly and the other one strictly increasingly on the whole domain of indices, that is, on the set of all positive natural numbers. Here, we present a complete picture on the monotonicity character of the one-parameter class of sequences of real numbers consisting of their convex combinations on the whole domain of indices.