Today I saw this problem on Medium: Compute the limit

Followed by “Pause the article and attempt a solution now.” (Don’t cheat and look ahead)

So I did. I do not really like factorials, so I immediately thought of Stirling’s approximation:

ln n! ≃ n ln n – n as n → ∞

and all of the n‘s cancelled, leaving the result 1/e. I then looked at the author’s solution. My answer was correct, but he used a completely different approach, as you can see. I posted my solution, and got a nice complement from him.

This is Thanksgiving day in the USA. I am thankful that my calculus skills are still pretty good decades after my last formal course in that or any related field .