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Déterminer la limite de suites arithmétiques définies par une relation de récurrence    ressource 3702

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

La suite ( v n ) n définie pour tout n par { v 0 = 7 10 v n + 1 = v n + 5 6 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["v", "0"], "\[LongEqual]", FractionBox["7", "10"]]], ""], List[RowBox[List[SubscriptBox["v", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List[SubscriptBox["v", "n"], "+", FractionBox["5", "6"]]]]], ""]], 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]] admet pour limite
La suite ( w n ) n définie pour tout n par { w 0 = 3 2 w n + 1 = w n + 10 3 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["w", "0"], "\[LongEqual]", FractionBox["3", "2"]]], ""], List[RowBox[List[SubscriptBox["w", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List[SubscriptBox["w", "n"], "+", FractionBox["10", "3"]]]]], ""]], 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]] admet pour limite
La suite ( x n ) n définie pour tout n par { x 0 = - 5 4 x n + 1 = x n + 1 3 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["x", "0"], "\[LongEqual]", RowBox[List["-", FractionBox["5", "4"]]]]], ""], List[RowBox[List[SubscriptBox["x", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List[SubscriptBox["x", "n"], "+", FractionBox["1", "3"]]]]], ""]], 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]] admet pour limite
La suite ( y n ) n définie pour tout n par { y 0 = - 3 5 y n + 1 = y n - 1 4 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["y", "0"], "\[LongEqual]", RowBox[List["-", FractionBox["3", "5"]]]]], ""], List[RowBox[List[SubscriptBox["y", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List[SubscriptBox["y", "n"], "-", FractionBox["1", "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]] admet pour limite
La suite ( z n ) n définie pour tout n par { z 0 = 2 5 z n + 1 = z n + 2 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["z", "0"], "\[LongEqual]", FractionBox["2", "5"]]], ""], List[RowBox[List[SubscriptBox["z", RowBox[List["n", "+", "1"]]], "\[LongEqual]", RowBox[List[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]] admet pour limite