grandes-ecoles 2012 QII.C.5

grandes-ecoles · France · centrale-maths2__mp Sequences and series, recurrence and convergence Closed-form expression derivation

We consider the sequence $x = (x_n)_{n \geqslant 0}$ defined by $$x_0 = 1, \quad x_1 = 1, \quad x_2 = 1, \quad x_3 = 0, \quad \text{and} \quad \forall n \in \mathbb{N}, x_{n+4} = x_{n+3} - 2x_{n+1}$$
We decide to modify only the value of $x_0$, by setting this time $x_0 = \frac{1}{2}$.
With this modification, quickly redo the study of questions II.C.2 and II.C.3.

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

We decide to modify only the value of $x_0$, by setting this time $x_0 = \frac{1}{2}$.

With this modification, quickly redo the study of questions II.C.2 and II.C.3.

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