grandes-ecoles 2019 Q17

grandes-ecoles · France · centrale-maths2__mp Sequences and Series Recurrence Relations and Sequence Properties

Let $n \in \mathbb{N}^{\star}$. Show that the application $$\Psi_n : \begin{gathered} \{0,1\}^n \rightarrow D_n \\ (x_j)_{j \in \llbracket 1,n \rrbracket} \mapsto \sum_{j=1}^{n} \frac{x_j}{2^j} \end{gathered}$$ is bijective.

Let $n \in \mathbb{N}^{\star}$. Show that the application
$$\Psi_n : \begin{gathered} \{0,1\}^n \rightarrow D_n \\ (x_j)_{j \in \llbracket 1,n \rrbracket} \mapsto \sum_{j=1}^{n} \frac{x_j}{2^j} \end{gathered}$$
is bijective.

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