Date: Feb 26, 2013 8:16 PM Author: John Reid Subject: inequality for sequence approaching e Let a(n) = (1+1/n)^n, n=1,2,3,...
It is well known that a(n)/e < 1, for all n.
On the other hand, we found for all n that
(1) n*ln(1+1/n) < a(n)/e.
As n goes to infinity, it is easy to see that the left side of (1) converges to 1.
The resulting sandwich yields the familiar fact that a(n) converges to e.
QUESTION: does anyone have a reference for (1) ???