Corrigé du 39 P. 45

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1. $u_{n+1} = qu_n$ donc $u_{n+1} = 2u_n$.

2. \[ \begin{aligned} &u_1 = 2u_0 = 2\times 3 = 6\;;&\\ &u_2 = 2u_1 = 2\times 6 = 12\;;&\\ &\boxed{u_3 = 2u_2 = 2\times 12 = 24\;;}&\\ &u_4 = 2u_3 = 2\times 24 = 48\;;&\\ &u_5 = 2u_4 = 2\times 48 = 96\;;&\\ &u_6 = 2u_5 = 2\times 96 =192\;;&\\ &u_7 = 2u_6 = 2\times 192 = 384\;;&\\ &u_8 = 2u_7 = 2\times 384 = 768\;;&\\ &u_9 = 2u_8 = 2\times 768 = 1536\;;&\\ &\boxed{u_{10} = 2u_9 = 2\times 1536 = 3072\;;}&\\ &u_{11} = 2u_{10} = 2\times 3072 = 6144\;;&\\ &u_{12} = 2u_{11} = 2\times 6144 = 12288\;;&\\ &\boxed{u_{13} = 2u_{12} = 2\times 12288 = 24576.}& \end{aligned} \]

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