The tutor discusses the limit, as n goes to infinity, of the nth root of n factorial.

It’s probably easy to agree that, for large n, n! > (n/6)^n.

lim_n→∞ ((n/6)^n)^(1/n) = lim_n→∞n/6 = ∞

Therefore,

lim_n→∞ (n!)^(1/n) = ∞, since for large n, n! > (n/6)^n.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.