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Topic: [MATHEDU] Proofs
Replies: 1   Last Post: Mar 4, 1998 12:51 PM

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Alvar J. Garcia

Posts: 304
Registered: 12/6/04
Re: [MATHEDU] Proofs
Posted: Mar 4, 1998 12:51 PM
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My AP Calc BBC, just investigated the sequence {(1+1/n)^n} as n --> inf
graphically (seq mode on the TI82) and algebraically (using L'Hopital) and
found: {(1+a/n)^n} = {((n+a)/n)^n} --> e^a as n --> inf (domain:pos ints).
We also let f(x) = (1+x)^(a/x) and showed that f(x) --> e^a as x --> 0
(domain: pos reals) by similar methods.

In computer science, we wrote programs to output convergence tables
confirming these results numerically!

Great fun...


On Mon, 2 Mar 1998, Prof William P Wardlaw wrote:
> Tony,
> I believe you meant (1 + 1/n) approaches 1 gives a convincing argument
> that (1 + 1/n)^n approaches 1 as well, rather than 0 in each case. Of
> course, I suspect that you must follow that since (1 + 1/n) > 1, there is
> an equally convincing argument that (1 + 1/n)^n approaches infinity, thus
> setting the stage for a proof.
> Bill
> This is an unmoderated distribution list discussing post-calculus teaching
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A. Jorge Garcia Teacher/Professor Mathematics/CompSci BaldwinSHS/NassauCC
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