p7.py

Created on March 22, 2022

532 Bytes

propriété combinaison 

Soit n un entier naturel alors 
somme (Z) entre k=0 et n (n k)=n

PREUVE 
Par définition, VkeN, 0<k<n, (nk) est le nbr de combinaison de k elements de E

cad (nk) est le nbr de parties de E composé de k elements
 
Une partie de E peut posserder 0;1;...;n 
d'élements pour keN, avec k<n,
le nbr de parties de k éléments
(nk)
le nbr total de parties de E 
est donc

card(P(E))
=(n0)+(n1)+(n2)+...+(nn)
= somme (Z) entre k=0 et n (nk)

Or card (P(E))=2^n
donc somme (Z) entre k=0 et n (nk)
=2^n

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