Improved convergence towards generalized Euler-Mascheroni constant

We propose new simple sequences approximating the Euler-Mascheroni constant and its generalization, which converge faster towards their limits than those considered by DeTemple [D.W. DeTemple, A quicker convergence to Euler's constant, Am. Math. Monthly 100 (5) (1998) 468-470], Sîntămărian [A. Sîntămărian, A generalization of Euler's constant, Numer. Algorithms 46 (2) (2007) 141-151] and Vernescu [A. Vernescu, A new accelerate convergence to the constant of Euler, Gazeta Matem., Ser. A, Bucharest XVII(XCVI) (4) (1999) 273-278].