(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 10729, 322] NotebookOptionsPosition[ 9525, 281] NotebookOutlinePosition[ 9960, 298] CellTagsIndexPosition[ 9917, 295] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Sequences and Series", "Title", CellChangeTimes->{{3.44193004827881*^9, 3.4419300539808683`*^9}}, TextAlignment->Center], Cell["\<\ by Ruth Dover Illinois Mathematics and Science Academy\ \>", "Subsubtitle", CellChangeTimes->{{3.692639887716036*^9, 3.69263990205936*^9}}], Cell[CellGroupData[{ Cell["Sequences", "Section", CellChangeTimes->{{3.441930113599506*^9, 3.441930117509397*^9}}], Cell[TextData[{ "For your sequence, enter ", StyleBox["kstart", FontSlant->"Italic"], " and ", StyleBox["kmax", FontSlant->"Italic"], ". Then enter the formula for your sequence as a function. An example is \ given, but these may be edited. 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The commands will show values of the sequence itself and \ the values of the sequence of partial sums. Then ", StyleBox["Mathematica", FontSlant->"Italic"], " will plot both." }], "Text", CellChangeTimes->{{3.441930822437107*^9, 3.441930829700968*^9}, { 3.441930874381027*^9, 3.44193102425307*^9}, {3.441931056453867*^9, 3.441931057623543*^9}, {3.441931245894719*^9, 3.44193124683749*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"b", ",", " ", "kstart", ",", " ", "kmax"}], "]"}]], "Input", CellChangeTimes->{{3.461362988595764*^9, 3.461362997822073*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"kstart", "=", "1"}], ";", " ", RowBox[{"kmax", "=", "50"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "k_", "]"}], ":=", FractionBox["1", "k"]}]}], "Input", CellChangeTimes->{{3.441931073722641*^9, 3.4419311132462683`*^9}, { 3.461362751406733*^9, 3.46136275963054*^9}}], Cell["Show the values of the terms of the original sequence.", "Text", CellChangeTimes->{{3.441931126948987*^9, 3.441931172430167*^9}, { 3.44193139275741*^9, 3.441931394149078*^9}}], Cell[BoxData[ RowBox[{"TableForm", 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