grandes-ecoles 2017 QI.A.3

grandes-ecoles · France · centrale-maths2__psi Sequences and series, recurrence and convergence Proof by induction on sequence properties
Verify that, if $\left( z _ { k } \right)$ is $p$-periodic, then $\forall n \in \mathbb { N } , \forall k \in \mathbb { N } , z _ { n + k p } = z _ { n }$. 
Verify that, if $\left( z _ { k } \right)$ is $p$-periodic, then $\forall n \in \mathbb { N } , \forall k \in \mathbb { N } , z _ { n + k p } = z _ { n }$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.A.5 QII.B.1 QII.B.2 QII.B.3 QII.C QII.D.1 QII.D.2 QII.E.1 QII.E.2 QII.E.3 QIII.A QIII.B.1 QIII.B.2 QIII.C QIII.D.1 QIII.D.2 QIII.E.1 QIII.E.2 QIII.E.3 QIV.A.1 QIV.A.2 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QV.A QV.B.1 QV.B.2 QV.B.3 QV.B.4