grandes-ecoles 2014 QI.B.3

grandes-ecoles · France · centrale-maths1__psi Sequences and series, recurrence and convergence Direct term computation from recurrence

We denote $V_n(z) = U_{n+1}(z, -1)$ for all $z \in \mathbb{C}$ and $n \in \mathbb{N}$, where $U(a,b) = (U_n(a,b))_{n \in \mathbb{N}}$ is the unique sequence satisfying $E_{a,b}$ with initial conditions $U_0(a,b) = 0$ and $U_1(a,b) = 1$. Explicitly write $V_1(z)$, $V_2(z)$ and $V_3(z)$ and determine their roots in $\mathbb{C}$.

We denote $V_n(z) = U_{n+1}(z, -1)$ for all $z \in \mathbb{C}$ and $n \in \mathbb{N}$, where $U(a,b) = (U_n(a,b))_{n \in \mathbb{N}}$ is the unique sequence satisfying $E_{a,b}$ with initial conditions $U_0(a,b) = 0$ and $U_1(a,b) = 1$.\\
Explicitly write $V_1(z)$, $V_2(z)$ and $V_3(z)$ and determine their roots in $\mathbb{C}$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.A.6 QI.A.7 QI.B.1 QI.B.2 QI.B.3 QI.B.4 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 QII.C.6 QII.C.7 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.B.5 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.C.5 QIII.C.6