Blake Whittaker
04/27/2023 · High School
On place un capital de \( 500 € \) sur un compte dont les intérêts annuels s'élèvent à \( 4 \% \) par an. On note \( u_{n} \) la valeur du capital après \( n \) années. 1) Calculer \( u_{2} \) et \( u_{3 .} \) 2) Quelle est la nature de la suite \( \left(u_{n}\right) \) ? On donnera son premier terme et sa raison. 3) Exprimer \( u_{n+1} \) en fonction de \( u_{n .} \) 4) Donner la variation de la suite \( \left(u_{n}\right) \). 5) Exprimer \( u_{n} \) en fonction de \( n \).
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1) \( u_{2} = 540,80 \, € \), \( u_{3} = 562,43 \, € \).
2) Suite géométrique, premier terme \( 500 \, € \), raison \( 1,04 \).
3) \( u_{n+1} = u_{n} \times 1,04 \).
4) Suite croissante.
5) \( u_{n} = 500 \times (1,04)^n \).
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