Vollständige Induktion Beweis Prinzip der vollständigen Induktion am Beispiel erklärt Bsp1

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Die vollständige Induktion ist ein Beweisverfahren, mit dem Du Aussagen für alle natürlichen Zahlen, die größer oder gleich einem Startwert sind, beweisen kannst. Die vollständige Induktion folgt einem ganz bestimmten Ablauf, den ich Dir in meinem Lernvideo gerne zeigen möchte. • 1. Induktionsanfang: • Beim Induktionsanfang ist es unser Ziel, nachzuweisen, dass die Aussagen für den Startwert gilt, also für das erste n, das wir einsetzen dürfen. Du setzt n auf der linken und rechten Seite der Behauptung ein und schaust, dass beide Seiten der Gleichung denselben Wert ergeben. • 2. Induktionsschritt • 2.1 Induktionsvoraussetzung • Die Induktionsvoraussetzung ist die eigentliche Behauptung. Es genügt also, wenn Du die Behauptung einfach nch einmal aufschreibst. • 2.2 Induktionsbehauptung • Die Induktionsbehauptung besagt folgendes: Wenn die Aussage für alle n wahr ist, dann ist sie auch für alle n+1 wahr. Du ersetzt also alle n aus der Behauptung durch n+1 • 2.3 Induktionsbeweis • im letzten Schritt, dem Induktionsbeweis, beweist Du die Induktionsbehauptung. Dabei splittest Du die Summe auf und setzt die Induktionsvoraussetzung ein. Ein wenig umformen und der Beweis ist erbracht. • Wenn Du Fragen hast, schreib sie gern in die Kommentare. Wenn Du etwas gelernt hast, zeig es mir gern durch ein Gefällt mir Liebe grüße, Dein Rick 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