nouveau     aide     guide     notions     brouillon     clavier     écran     imprimer
Déterminer la limite de suites géométriques de raison positive définies par une relation de récurrence    ressource 1730

Indiquez la limite de chacune des suites géométriques définies ci-dessous.

La suite ( v n ) n définie pour tout n par { v 0 = 4 3 v n + 1 = 7 v n 2 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["v", "0"], "\[LongEqual]", FractionBox["4", "3"]]], ""], List[RowBox[List[SubscriptBox["v", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[RowBox[List["7", " ", SubscriptBox["v", "n"]]], "2"]]], ""]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic], Rule[AllowedDimensions, List[2, Automatic]], Rule[Selectable, True], Rule[Editable, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 0.5`], Rule[ColumnWidths, Automatic]], "Piecewise", Rule[SyntaxForm, Equal], Rule[SelectWithContents, True], Rule[Selectable, False], Rule[Editable, False], Rule[DeleteWithContents, True]]
La suite ( w n ) n définie pour tout n par { w 0 = - 1 9 w n + 1 = 7 w n 4 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["w", "0"], "\[LongEqual]", RowBox[List["-", FractionBox["1", "9"]]]]], ""], List[RowBox[List[SubscriptBox["w", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[RowBox[List["7", " ", SubscriptBox["w", "n"]]], "4"]]], ""]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic], Rule[AllowedDimensions, List[2, Automatic]], Rule[Selectable, True], Rule[Editable, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 0.5`], Rule[ColumnWidths, Automatic]], "Piecewise", Rule[SyntaxForm, Equal], Rule[SelectWithContents, True], Rule[Selectable, False], Rule[Editable, False], Rule[DeleteWithContents, True]]
La suite ( x n ) n définie pour tout n par { x 0 = 3 10 x n + 1 = x n 10 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["x", "0"], "\[LongEqual]", FractionBox["3", "10"]]], ""], List[RowBox[List[SubscriptBox["x", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[SubscriptBox["x", "n"], "10"]]], ""]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic], Rule[AllowedDimensions, List[2, Automatic]], Rule[Selectable, True], Rule[Editable, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 0.5`], Rule[ColumnWidths, Automatic]], "Piecewise", Rule[SyntaxForm, Equal], Rule[SelectWithContents, True], Rule[Selectable, False], Rule[Editable, False], Rule[DeleteWithContents, True]]
La suite ( y n ) n définie pour tout n par { y 0 = 7 8 y n + 1 = 3 y n 5 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["y", "0"], "\[LongEqual]", FractionBox["7", "8"]]], ""], List[RowBox[List[SubscriptBox["y", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[RowBox[List["3", " ", SubscriptBox["y", "n"]]], "5"]]], ""]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic], Rule[AllowedDimensions, List[2, Automatic]], Rule[Selectable, True], Rule[Editable, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 0.5`], Rule[ColumnWidths, Automatic]], "Piecewise", Rule[SyntaxForm, Equal], Rule[SelectWithContents, True], Rule[Selectable, False], Rule[Editable, False], Rule[DeleteWithContents, True]]
La suite ( z n ) n définie pour tout n par { z 0 = - 6 7 z n + 1 = 9 z n 2 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["z", "0"], "\[LongEqual]", RowBox[List["-", FractionBox["6", "7"]]]]], ""], List[RowBox[List[SubscriptBox["z", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[RowBox[List["9", " ", SubscriptBox["z", "n"]]], "2"]]], ""]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic], Rule[AllowedDimensions, List[2, Automatic]], Rule[Selectable, True], Rule[Editable, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 0.5`], Rule[ColumnWidths, Automatic]], "Piecewise", Rule[SyntaxForm, Equal], Rule[SelectWithContents, True], Rule[Selectable, False], Rule[Editable, False], Rule[DeleteWithContents, True]]