grandes-ecoles 2011 QII.A.2

grandes-ecoles · France · centrale-maths1__mp Sequences and Series Properties and Manipulation of Power Series or Formal Series
Show that $a _ { 0 } = 1$ and that for every $p \geqslant 1 , a _ { p } = - \sum _ { i = 2 } ^ { p + 1 } \frac { a _ { p + 1 - i } } { i ! }$. Deduce that $\left| a _ { p } \right| \leqslant 1$ for every natural integer $p$. Determine $a _ { 1 }$ and $a _ { 2 }$. 
Show that $a _ { 0 } = 1$ and that for every $p \geqslant 1 , a _ { p } = - \sum _ { i = 2 } ^ { p + 1 } \frac { a _ { p + 1 - i } } { i ! }$. Deduce that $\left| a _ { p } \right| \leqslant 1$ for every natural integer $p$. Determine $a _ { 1 }$ and $a _ { 2 }$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.B.1 QI.B.2 QI.B.3 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIV.A.1 QIV.A.2 QIV.A.3 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.C.1 QIV.C.2