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Finding a formula for a sum

• To: mathgroup at smc.vnet.net
• Subject: [mg35104] Finding a formula for a sum
• From: Matthias.Bode at oppenheim.de
• Date: Tue, 25 Jun 2002 03:39:48 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Dear Colleagues,

when trying to find the number of diagonals in a convex polygon (all corners
on the perimeter of a circle) with n corners I came across that sum:

+(n-3) ; up to here = diagonals in a triangle.

+(n-3) ; up to here = diagonals in a quadrangle.

+(n-4) ; up to here = diagonals in a pentagon.

+(n-5) ; up to here = diagonals in a hexagon.

+(n-6) ; up to here = diagonals in a heptagon.
and so on.

I found the general formula (n*n -3*n)/2 with pencil and paper.

How could I coax MATHEMATICA into helping me to find the generalization in
this case - and of course for more difficult ones as well?

Best regards,
Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 95 380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de