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mohamedmelouki25
@mohamedmelouki25
January 2021
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Bonjour
Svp
Dèmontrer que :
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scoladan
Verified answer
Bonjour,
par récurrence :
(1+x)^1 = 1 + x ==> initialisation ok
On suppose la propriété vraie au rang n
(1+x)^n+1 = (1+x)(1+x)^n >= (x+1)(1 + nx)
(x+1)(1 + nx) = 1 + (n+1)x + nx^2 <= 1 + (n+1)x car nx^2 >= 0
==> (1+x)^n+1 >= 1 + (n+1)x
==> Propriété héritée
2 votes
Thanks 1
mohamedmelouki25
(x+1)(1+nx) ??????
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Lista de comentários
Verified answer
Bonjour,par récurrence :
(1+x)^1 = 1 + x ==> initialisation ok
On suppose la propriété vraie au rang n
(1+x)^n+1 = (1+x)(1+x)^n >= (x+1)(1 + nx)
(x+1)(1 + nx) = 1 + (n+1)x + nx^2 <= 1 + (n+1)x car nx^2 >= 0
==> (1+x)^n+1 >= 1 + (n+1)x
==> Propriété héritée