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Déterminer la limite, lorsqu'elle existe, de suites géométriques définies par une relation de récurrence    ressource 3704

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

La suite ( v n ) n définie pour tout n par { v 0 = - 4 5 v n + 1 = - 3 v n 7 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["v", "0"], "\[LongEqual]", RowBox[List["-", FractionBox["4", "5"]]]]], ""], List[RowBox[List[SubscriptBox["v", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List["-", FractionBox[RowBox[List["3", " ", SubscriptBox["v", "n"]]], "7"]]]]], ""]], 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 = 8 5 w n + 1 = - 2 w n 5 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["w", "0"], "\[LongEqual]", FractionBox["8", "5"]]], ""], List[RowBox[List[SubscriptBox["w", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SubscriptBox["w", "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 ( x n ) n définie pour tout n par { x 0 = - 7 x n + 1 = 9 x n TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["x", "0"], "\[LongEqual]", RowBox[List["-", "7"]]]], ""], List[RowBox[List[SubscriptBox["x", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List["9", " ", SubscriptBox["x", "n"]]]]], ""]], 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 = 4 y n + 1 = - 7 y n 5 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["y", "0"], "\[LongEqual]", "4"]], ""], List[RowBox[List[SubscriptBox["y", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List["-", FractionBox[RowBox[List["7", " ", 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 = 9 2 z n + 1 = - 4 z n TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["z", "0"], "\[LongEqual]", FractionBox["9", "2"]]], ""], List[RowBox[List[SubscriptBox["z", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List[RowBox[List["-", "4"]], " ", SubscriptBox["z", "n"]]]]], ""]], 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]]