Cruz Hobbs
11/30/2023 · Senior High School
On suppose que la suite \( \left(u_{n}\right) \) est définie par \( \left\{\begin{array}{l}u_{0}=0 \\ u_{n+1}=1,2 u_{n}+5000\end{array}\right. \) et que le modèle est une bonne estimation du nombre d'écrans vendus par la suite. a) Déterminer la formule explicite de la suite \( \left(u_{n}\right) \). b) Déterminer la limite de la suite \( \left(u_{n}\right) \) et interpréter ce résultat.
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a) La formule explicite de la suite \( (u_n) \) est \( u_n = 25000 \cdot (1.2)^n - 25000 \).
b) La limite de la suite \( (u_n) \) est infinie, ce qui signifie que le nombre d'écrans vendus augmente sans borne au fil du temps.
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