recu.py

Created by comecp

Created on October 17, 2023

545 Bytes

Soit Un: U0=
         Un+1=

Pour tout entier naturel n, 
on pose (Pn): "Un="

  Initialisation(n=)
  On a : U0=
         Un=

  Donc Pn est:vrai pour n=0

  Hérédité: Soit n un entier naturel
  Supposons que Pn est vraie, c.a.d : Un=
  Montrons que Pn+1 est vraie, c.a.d :Un+1=

  On a par hypothèse de récurence : Un=Un+1

  Donc Pn+1 est vraie

  Conclusion : La proposition est 
  initialisé au rang ... 0 et est
  hereditaire.
  D'apres le principe de 
  récurrence on generalise
  et Pour tout n : 
  Pn équivaut a  Un=

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