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Re: [MATHEDU] Proofs
Posted:
Mar 4, 1998 12:51 PM


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...
Regards
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 postcalculus teaching > and learning of mathematics.David.Epstein@warwick.ac.uk > > Get guidelines before posting: email majordomo@warwick.ac.uk saying > get mathedu guidelines > (Un)subscribe to mathedu(digest)by email to majordomo@warwick.ac.uk saying: > (un)subscribe mathedu(digest) <type in your email address here> >
A. Jorge Garcia Teacher/Professor Mathematics/CompSci BaldwinSHS/NassauCC ========================================================================= The Calculus Page http://freenet.buffalo.edu/~aj317 WorkBook Orders mailto:sffbookclub@compuserve.com All Other EMail mailto:aj317@freenet.buffalo.edu *************************************************************************



