exercice_recurrence.py

Created by vovenastream

Created on September 22, 2024

716 Bytes

demontrer que pour tout n>5.on a 2n>n**2
-initialisation:pour n=5: 2**5=32
                           5**2=25
            on a : 2**5>5**2
            la propriete est vrai pour n=5    
-heredite
 .hypothese de recurrence: soit un entier k>5
 tel que la propriete soit vrai 2**K>k**2
 .a demontrer: 2**k+1>(k+1)**2
 on a : 2**k>k**2 d'apres HR
 2**k*2**1>2k**2
 2**k+1>2k**2
 demontrons que 2k**2>(k+1)**2
 soit 2k**2>k**2+2k+1
 k**2-2k-1>0
 delta=4-4*(-1)=8
 delta positif donc -b-+VD/2
 delata neg pas solu
 delta nul -b/2a
 
conclusion: 
  la propriete est vrai pour n=5 et
  hereditaire a partir de ce rang 
  d'apres le principe de recurrence
  elle est vrai pour tout entier
  n>5

During your visit to our site, NumWorks needs to install "cookies" or use other technologies to collect data about you in order to:

With the exception of Cookies essential to the operation of the site, NumWorks leaves you the choice: you can accept Cookies for audience measurement by clicking on the "Accept and continue" button, or refuse these Cookies by clicking on the "Continue without accepting" button or by continuing your browsing. You can update your choice at any time by clicking on the link "Manage my cookies" at the bottom of the page. For more information, please consult our cookies policy.

Accept and continue Continue without accepting