grandes-ecoles 2017 QI.B.1

grandes-ecoles · France · centrale-maths2__pc Sequences and Series Limit Evaluation Involving Sequences

Let $k$ be a strictly positive integer and $q$ a real belonging to the interval $]0,1[$. Show that the sequences $\left(\frac{1}{(n+1)^{k}}\right)_{n \in \mathbb{N}},\left(n^{k} q^{n}\right)_{n \in \mathbb{N}}$ and $\left(\frac{1}{n !}\right)_{n \in \mathbb{N}}$ belong to $E^{c}$ and give their convergence rate.

Let $k$ be a strictly positive integer and $q$ a real belonging to the interval $]0,1[$. Show that the sequences $\left(\frac{1}{(n+1)^{k}}\right)_{n \in \mathbb{N}},\left(n^{k} q^{n}\right)_{n \in \mathbb{N}}$ and $\left(\frac{1}{n !}\right)_{n \in \mathbb{N}}$ belong to $E^{c}$ and give their convergence rate.

Paper Questions

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