grandes-ecoles 2012 QII.C.2

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

We consider the sequence $x = (x_n)_{n \geqslant 0}$ defined by $$x_0 = 1, \quad x_1 = 1, \quad x_2 = 1, \quad x_3 = 0, \quad \text{and} \quad \forall n \in \mathbb{N}, x_{n+4} = x_{n+3} - 2x_{n+1}$$
Specify the rank of $H_n(x)$ for any integer $n$ in $\mathbb{N}^*$ and indicate the minimal order of the sequence $x$.

We consider the sequence $x = (x_n)_{n \geqslant 0}$ defined by
$$x_0 = 1, \quad x_1 = 1, \quad x_2 = 1, \quad x_3 = 0, \quad \text{and} \quad \forall n \in \mathbb{N}, x_{n+4} = x_{n+3} - 2x_{n+1}$$

Specify the rank of $H_n(x)$ for any integer $n$ in $\mathbb{N}^*$ and indicate the minimal order of the sequence $x$.

Paper Questions

QI.A QI.B.1 QI.B.2 QI.C.1 QI.C.2 QI.C.3 QI.D QII.A.1 QII.A.2 QII.B.1 QII.B.2 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QIII.A.1 QIII.A.2 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.C.1 QIII.C.2 QIII.D.1 QIII.D.2 QIII.D.3