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Déterminer le sens de variation de suites géométriques à termes positifs définies par une relation de récurrence    ressource 2538

Indiquez le sens de variation de chacune des suites géométriques définies ci-dessous.

La suite ( v n ) n définie pour tout n par { v 0 = 2 7 v n + 1 = v n 10 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["v", "0"], "\[LongEqual]", FractionBox["2", "7"]]], ""], List[RowBox[List[SubscriptBox["v", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[SubscriptBox["v", "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 ( w n ) n définie pour tout n par { w 0 = 5 2 w n + 1 = 5 w n 4 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["w", "0"], "\[LongEqual]", FractionBox["5", "2"]]], ""], List[RowBox[List[SubscriptBox["w", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[RowBox[List["5", " ", 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 = 10 9 x n + 1 = 9 x n 8 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["x", "0"], "\[LongEqual]", FractionBox["10", "9"]]], ""], List[RowBox[List[SubscriptBox["x", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[RowBox[List["9", " ", SubscriptBox["x", "n"]]], "8"]]], ""]], 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 = 10 7 y n + 1 = y n 6 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["y", "0"], "\[LongEqual]", FractionBox["10", "7"]]], ""], List[RowBox[List[SubscriptBox["y", RowBox[List["n", "+", "1"]]], "\[LongEqual]", FractionBox[SubscriptBox["y", "n"], "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]]
La suite ( z n ) n définie pour tout n par { z 0 = 9 z n + 1 = 9 z n 2 TagBox[GridBox[List[List["\[Piecewise]", GridBox[List[List[RowBox[List[SubscriptBox["z", "0"], "\[LongEqual]", "9"]], ""], 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]]