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John Reid
Posts:
1
From:
Costa Rica
Registered:
2/26/13


inequality for sequence approaching e
Posted:
Feb 26, 2013 8:16 PM


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) ???



