General asymptotic growth question

Question

Show that n! = o(nⁿ)  for positive n

Answer 1

You should check out the development of Stirling's approximation n! ∼ (2π)^1/2n^n+1/2e^-n where the ∼ is used to indicate that the ratio of the 2 sides tends to 1  as n → ∞.

 

Check WIlliam Feller "An Introduction to Probability Theory and Its Applications", Vol I, written long ago but still a standard reference.