grandes-ecoles 2016 QIII.A.2

grandes-ecoles · France · centrale-maths2__pc Proof Computation of a Limit, Value, or Explicit Formula

We consider the family of polynomials $$\left\{ \begin{array}{l} H_0 = 1 \\ H_k = \frac{1}{k!} \prod_{j=0}^{k-1} (X - j) \quad \text{for } k \in \llbracket 1, n \rrbracket \end{array} \right.$$
Calculate $\delta\left(H_0\right)$ and, for $k \in \llbracket 1, n \rrbracket$, express $\delta\left(H_k\right)$ in terms of $H_{k-1}$.

We consider the family of polynomials
$$\left\{ \begin{array}{l} H_0 = 1 \\ H_k = \frac{1}{k!} \prod_{j=0}^{k-1} (X - j) \quad \text{for } k \in \llbracket 1, n \rrbracket \end{array} \right.$$

Calculate $\delta\left(H_0\right)$ and, for $k \in \llbracket 1, n \rrbracket$, express $\delta\left(H_k\right)$ in terms of $H_{k-1}$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.A.6 QI.A.7 QI.A.8 QI.A.9 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.B.5 QI.B.6 QI.B.7 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.A.5 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.C.5 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3