grandes-ecoles 2012 QI.B.2

grandes-ecoles · France · centrale-maths2__mp Sequences and Series Recurrence Relations and Sequence Properties
We consider the sequence $x$ defined by $x_0 = 0, x_1 = -1, x_2 = 2$ and by the linear recurrence relation of order 3: $\forall n \in \mathbb{N}, x_{n+3} = -3x_{n+2} - 3x_{n+1} - x_n$.
Determine the minimal polynomial (and thus the minimal order) of the sequence $x$. 
We consider the sequence $x$ defined by $x_0 = 0, x_1 = -1, x_2 = 2$ and by the linear recurrence relation of order 3: $\forall n \in \mathbb{N}, x_{n+3} = -3x_{n+2} - 3x_{n+1} - x_n$.

Determine the minimal polynomial (and thus 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