IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-658-09990-9_26.html
   My bibliography  Save this book chapter

Empirische Mathematik: Die Methode (!) „Rate und Prüfe“

In: Alles Mathematik

Author

Listed:
  • Shalosh B. Ekhad

    (Rutgers University (New Brunswick), Department of Mathematics)

  • Doron Zeilberger

    (Rutgers University (New Brunswick), Department of Mathematics)

Abstract

Zusammenfassung Wir alle kennen die Geschichte, wie der junge Carl Friedrich Gauß angeblich die ersten 100 Zahlen aufaddierte, indem er einen „genialen“ Trick anwandte: Er addierte 1 und 100, dann 2 und 99, 3 und 98, und so weiter. Sein Trick wäre aber kläglich gescheitert, falls die Aufgabe gelautet hätte, die ersten 100 Quadrate aufzusummieren. Eine viel bessere Methode wäre für ihn gewesen, die ersten paar Terme der Folge a(n) := 1 +2 + · · · + n zu berechnen a(0) = 0 , a(1) = 1 , a(2) = 3 , a(3) = 6 , a(4) = 10 , dann sein Genie zu verwenden, um das dahinter liegende Muster zu entdecken, nämlich a(0) = (0 · 1)/2 , a(1) = (1 · 2)/2 , a(2) = (2 · 3)/2 , a(3) = (3 · 4)/2 , a(4) = (4 · 5)/2 , und dann die Vermutung a(n) = n(n + 1)/2 aufzustellen. Er hätte noch einige weitere Werte, sagen wir n = 5 und n = 6, testen können und daraus geschlossen, dass a(100) = (100 · 101)/2 = 5050 ist (vgl. [Z1]).

Suggested Citation

  • Shalosh B. Ekhad & Doron Zeilberger, 2016. "Empirische Mathematik: Die Methode (!) „Rate und Prüfe“," Springer Books, in: Martin Aigner & Ehrhard Behrends (ed.), Alles Mathematik, edition 4, pages 441-456, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-09990-9_26
    DOI: 10.1007/978-3-658-09990-9_26
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-658-09990-9_26. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.