What it amounts to is whitttling it down to:
A take on the famous limit of e:
Now, if you take the sum of
Does anyone know how to show this limit?
limit as n approaches infinity of the summation from k = 0 to n of [(n-k)/n]^n.
The summation is just the gamma symbol with k = 0 on the bottom and n on the top. Apparently, the limit equals e/(e-1), but how would you show it with algebra?