The Euler-Mascheroni constant can be computed by evaluating an equation with a large n, but convergence is slow and rounding errors accumulate.
A more efficient approach involves adding an extra factor of ½ in the log term, which converges faster to the Euler-Mascheroni constant.
Comparing the two methods, the error in the first method with n = 4000 is similar to the error in the second method with n = 16.
Software like y-cruncher has been used to set world records for computing constants like π and the Euler-Mascheroni Constant, which is particularly challenging to compute.