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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 56646, 1621]*) (*NotebookOutlinePosition[ 57317, 1645]*) (* CellTagsIndexPosition[ 57273, 1641]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Examples for Section 8.2 Calculating Limits of Sequences\ \>", "Subsection"], Cell[CellGroupData[{ Cell["p. 628", "Subsection"], Cell[CellGroupData[{ Cell["1.", "Subsubsection"], Cell[BoxData[ \(\(a[n_]\ := \ 2\ + \ 0.1\^n; \)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(z\ = \ Table[a[n], \ {n, 1, 10}]\)], "Input"], Cell[BoxData[ \({2.10000000000000008`, 2.00999999999999978`, 2.00099999999999988`, 2.00010000000000021`, 2.00001000000000006`, 2.00000100000000013`, 2.00000009999999983`, 2.00000000999999993`, 2.00000000100000008`, 2.0000000001`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[a[n], n \[Rule] \[Infinity]]\)], "Input"], Cell[BoxData[ \(2\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["5.", "Subsubsection"], Cell[BoxData[ \(\(a[n_]\ := \ N[\(1 - 5 n\^4\)\/\(n\^4 + 8 n\^3\)]; 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