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dodo11
@dodo11
January 2021
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Bonsoir j'ai un exo de math sur la récurrence des suites et exponentielle Niveau terminale
Aidez moi merci d'avance
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scoladan
Verified answer
Bonjour,
on vérifie U1 = (0 + e^3 - 1)/e^3 = 1 - 1/e^3 = 1 - e^(-3)
Un+1 = (Un + e^3 - 1)/e^3
= (1 - e^-3n + e^3 - 1)/e^3
= -e^-3n/e^3 + e^3/e^3
= 1 - e^(-3n-3)
= 1 - e^-3(n+1)
==> hérédité démontrée
1 votes
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dodo11
merci
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Lista de comentários
Verified answer
Bonjour,on vérifie U1 = (0 + e^3 - 1)/e^3 = 1 - 1/e^3 = 1 - e^(-3)
Un+1 = (Un + e^3 - 1)/e^3
= (1 - e^-3n + e^3 - 1)/e^3
= -e^-3n/e^3 + e^3/e^3
= 1 - e^(-3n-3)
= 1 - e^-3(n+1)
==> hérédité démontrée