(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 12317, 443] NotebookOptionsPosition[ 10550, 377] NotebookOutlinePosition[ 10929, 394] CellTagsIndexPosition[ 10886, 391] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Lesson 7 Answers - Sums, Series, Products and Limits", "Section", CellChangeTimes->{ 3.4610864122323008`*^9, {3.461268729551034*^9, 3.4612687554944*^9}, { 3.4651303620378027`*^9, 3.465130362914732*^9}}], Cell[TextData[{ "1) Use ", StyleBox["Mathematica", FontSlant->"Italic"], " to determine the following limits. 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See the Documentation Center." }], "Text", CellChangeTimes->{{3.449231595579927*^9, 3.4492316074228983`*^9}, { 3.449231644937571*^9, 3.4492317014154387`*^9}, 3.461105920058*^9}, FontSlant->"Italic"], Cell[CellGroupData[{ Cell[TextData[{ "(b) ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"n", "=", "1"}], "100"], FractionBox["1", SuperscriptBox["n", "3"]]}], FontSize->16], TraditionalForm]]] }], "Subsubsection", CellDingbat->None, CellChangeTimes->{{3.417733323845963*^9, 3.4177333306696243`*^9}, { 3.449231470575086*^9, 3.449231482462484*^9}}, FontWeight->"Plain"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"second", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"1", "/", RowBox[{"n", "^", "3"}]}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "100"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.449231514922411*^9, 3.449231556399645*^9}}, FontSlant->"Italic"], Cell[BoxData[ RowBox[{"81473483330743503583074181861672511931518122336172216406894149391331\ 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following:\n(a) ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ FractionBox[ StyleBox["1", FontSize->12], "2"], "\[Times]", FractionBox["3", "4"], "\[Times]", FractionBox["5", "6"], "\[Times]", FractionBox["7", "8"], "\[Times]"}], FontSize->16], TraditionalForm]]], "...", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{"\[Times]", FractionBox["97", "98"], "\[Times]", FractionBox["99", "100"]}], FontSize->16], TraditionalForm]]] }], "Text", CellChangeTimes->{{3.4492317398502407`*^9, 3.449231742048436*^9}, { 3.4611060361453533`*^9, 3.461106037250887*^9}}, FontWeight->"Plain"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"first", " ", "=", RowBox[{"Product", "[", RowBox[{ RowBox[{"n", "/", RowBox[{"(", RowBox[{"n", "+", "1"}], ")"}]}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "99", ",", "2"}], "}"}]}], "]"}]}]], "Input",\ CellChangeTimes->{{3.449231774848055*^9, 3.449231886011821*^9}}, FontSlant->"Italic"], Cell[BoxData[ FractionBox["12611418068195524166851562157", 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CellChangeTimes->{{3.4492317541120768`*^9, 3.449231756624103*^9}}, FontWeight->"Plain"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{"first", "-", "second"}], "]"}]], "Input", FontSlant->"Italic"], Cell[BoxData["0.05436421920881796`"], "Output", CellChangeTimes->{3.449231914281698*^9}, FontSlant->"Italic"] }, Open ]], Cell[TextData[{ "4) Can ", StyleBox["Sum", "Input"], " be used to calculate the sum of a sequence of vectors? " }], "Text", CellChangeTimes->{{3.461106195941146*^9, 3.4611062519476337`*^9}, { 3.46110631672115*^9, 3.4611063509631577`*^9}, 3.461106417875456*^9}], Cell["\<\ Yes. For example, the following calculates (1,0)+(2,1)+(3,2)+(4,3).\ \>", "Text", CellChangeTimes->{{3.461106423621437*^9, 3.4611065145863123`*^9}}, FontSlant->"Italic"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Sum", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"i", "-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "4"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.461106266592536*^9, 3.461106294104004*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"10", ",", "6"}], "}"}]], "Output", CellChangeTimes->{3.461106295376676*^9}] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{780, 681}, WindowMargins->{{117, Automatic}, {103, Automatic}}, ShowSelection->True, Magnification->1., FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (April 20, 2007)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 216, 3, 67, "Section"], Cell[809, 28, 566, 18, 53, "Text"], Cell[CellGroupData[{ Cell[1400, 50, 308, 9, 27, "Input"], Cell[1711, 61, 152, 3, 45, "Output"] }, Open ]], Cell[1878, 67, 367, 14, 40, "Text"], Cell[CellGroupData[{ Cell[2270, 85, 339, 10, 27, "Input"], Cell[2612, 97, 114, 3, 44, "Output"] }, Open ]], Cell[2741, 103, 546, 18, 55, "Text"], Cell[CellGroupData[{ Cell[3312, 125, 314, 9, 27, "Input"], Cell[3629, 136, 122, 3, 27, "Output"] }, Open ]], Cell[3766, 142, 340, 7, 26, "Text"], Cell[CellGroupData[{ Cell[4131, 153, 427, 15, 39, "Subsubsection"], Cell[CellGroupData[{ Cell[4583, 172, 310, 9, 27, "Input"], Cell[4896, 183, 387, 6, 73, "Output"] }, Open ]], Cell[5298, 192, 286, 7, 26, "Text"], Cell[CellGroupData[{ Cell[5609, 203, 174, 4, 27, "Input"], Cell[5786, 209, 113, 2, 27, "Output"] }, Open ]], Cell[5914, 214, 748, 27, 55, "Text"], Cell[CellGroupData[{ Cell[6687, 245, 356, 11, 27, "Input"], Cell[7046, 258, 223, 5, 45, "Output"] }, Open ]], Cell[7284, 266, 728, 26, 40, "Text"], Cell[CellGroupData[{ Cell[8037, 296, 355, 11, 27, "Input"], Cell[8395, 309, 727, 11, 133, "Output"] }, Open ]], Cell[9137, 323, 237, 6, 26, "Text"], Cell[CellGroupData[{ Cell[9399, 333, 108, 3, 27, "Input"], Cell[9510, 338, 111, 2, 27, "Output"] }, Open ]], Cell[9636, 343, 267, 6, 26, "Text"], Cell[9906, 351, 181, 4, 26, "Text"], Cell[CellGroupData[{ Cell[10112, 359, 279, 8, 27, "Input"], Cell[10394, 369, 116, 3, 27, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)