Some new sequences that converge to a generalized Euler constant

The purpose of the paper is to give some sequences that converge quickly to a generalized Euler constant, i.e. the limit of the sequence (1as+1(a+1)s+⋯+1(a+n−1)s−11−s((a+n−1)1−s−a1−s))n∈N, where a∈(0,+∞)a∈(0,+∞) and s∈(0,1)s∈(0,1).