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Topic: inequality for sequence approaching e
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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
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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) ???

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