The discussion focuses on proving that the limit of ((2^n * n!)/n^n) approaches zero as n approaches infinity. Participants suggest using Stirling's approximation to simplify the factorial term, which helps in analyzing the logarithm of the limit. By applying the continuity of the logarithm function, the logarithm can be pulled inside the limit for easier manipulation. The approximation of log(n!) using Stirling's formula allows for simplification, leading to a conclusion about the limit. Ultimately, the discussion emphasizes the importance of careful logarithmic manipulation and approximation techniques in limit proofs.