(* 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[      7398,        251]
NotebookOptionsPosition[      6849,        227]
NotebookOutlinePosition[      7191,        242]
CellTagsIndexPosition[      7148,        239]
WindowFrame->Normal
ContainsDynamic->False*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"k", "=", "1"}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pa"}], ")"}], "A"}], "+", 
         RowBox[{"pn", " ", "B1"}]}], "\[Equal]", "R"}], ",", 
       RowBox[{
        RowBox[{
         RowBox[{"pn", " ", "A"}], "+", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pb"}], ")"}], " ", "B1"}]}], "\[Equal]", 
        "R"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"A", ",", "B1"}], "}"}]}], "]"}], "//", "Simplify"}]}]], "Input",\

 CellChangeTimes->{{3.567941891817825*^9, 3.5679419571754246`*^9}, {
  3.567942031391925*^9, 3.567942031639925*^9}, {3.567942232279525*^9, 
  3.5679422376165247`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"A", "\[Rule]", 
     FractionBox[
      RowBox[{"pb", " ", "R"}], 
      RowBox[{
       RowBox[{"pb", " ", "pn"}], "+", 
       RowBox[{"pa", " ", 
        RowBox[{"(", 
         RowBox[{"pb", "+", "pn"}], ")"}]}]}]]}], ",", 
    RowBox[{"B1", "\[Rule]", 
     FractionBox[
      RowBox[{"pa", " ", "R"}], 
      RowBox[{
       RowBox[{"pb", " ", "pn"}], "+", 
       RowBox[{"pa", " ", 
        RowBox[{"(", 
         RowBox[{"pb", "+", "pn"}], ")"}]}]}]]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{{3.567941942390525*^9, 3.567941958221425*^9}, 
   3.567942032384925*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"k", "=", "2"}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pa"}], ")"}], "A"}], "+", 
         RowBox[{"pn", " ", "B1"}], "+", 
         RowBox[{"pn", " ", "B2"}]}], "\[Equal]", "R"}], ",", 
       RowBox[{
        RowBox[{
         RowBox[{"pn", " ", "A"}], "+", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pb"}], ")"}], " ", "B1"}], "+", 
         RowBox[{"pn", " ", "B2"}]}], "\[Equal]", "R"}], ",", " ", 
       RowBox[{
        RowBox[{
         RowBox[{"pn", " ", "A"}], " ", "+", " ", 
         RowBox[{"pn", " ", "B1"}], " ", "+", " ", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pb"}], ")"}], " ", "B2"}]}], "\[Equal]", 
        "R"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"A", ",", "B1", ",", "B2"}], "}"}]}], "]"}], "//", 
   "Simplify"}]}]], "Input",
 CellChangeTimes->{{3.5679422440475245`*^9, 3.5679422965371246`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"A", "\[Rule]", 
     FractionBox[
      RowBox[{"pb", " ", "R"}], 
      RowBox[{
       RowBox[{"pa", " ", "pb"}], "+", 
       RowBox[{"2", " ", "pa", " ", "pn"}], "+", 
       RowBox[{"pb", " ", "pn"}]}]]}], ",", 
    RowBox[{"B1", "\[Rule]", 
     FractionBox[
      RowBox[{"pa", " ", "R"}], 
      RowBox[{
       RowBox[{"pa", " ", "pb"}], "+", 
       RowBox[{"2", " ", "pa", " ", "pn"}], "+", 
       RowBox[{"pb", " ", "pn"}]}]]}], ",", 
    RowBox[{"B2", "\[Rule]", 
     FractionBox[
      RowBox[{"pa", " ", "R"}], 
      RowBox[{
       RowBox[{"pa", " ", "pb"}], "+", 
       RowBox[{"2", " ", "pa", " ", "pn"}], "+", 
       RowBox[{"pb", " ", "pn"}]}]]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.567942297328125*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"k", "=", "3"}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pa"}], ")"}], "A"}], "+", 
         RowBox[{"pn", " ", "B1"}], "+", 
         RowBox[{"pn", " ", "B2"}], "+", 
         RowBox[{"pn", " ", "B3"}]}], "\[Equal]", "R"}], ",", 
       RowBox[{
        RowBox[{
         RowBox[{"pn", " ", "A"}], "+", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pb"}], ")"}], " ", "B1"}], "+", 
         RowBox[{"pn", " ", "B2"}], "+", 
         RowBox[{"pn", " ", "B3"}]}], "\[Equal]", "R"}], ",", " ", 
       RowBox[{
        RowBox[{
         RowBox[{"pn", " ", "A"}], " ", "+", " ", 
         RowBox[{"pn", " ", "B1"}], " ", "+", " ", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pb"}], ")"}], " ", "B2"}], "+", 
         RowBox[{"pn", " ", "B3"}]}], "\[Equal]", "R"}], ",", " ", 
       RowBox[{
        RowBox[{
         RowBox[{"pn", " ", "A"}], " ", "+", " ", 
         RowBox[{"pn", " ", "B1"}], " ", "+", " ", 
         RowBox[{"pn", " ", "B2"}], "+", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"pn", "+", "pb"}], ")"}], "B3"}]}], "\[Equal]", "R"}]}], 
      "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"A", ",", "B1", ",", "B2", ",", "B3"}], "}"}]}], "]"}], "//", 
   "Simplify"}]}]], "Input",
 CellChangeTimes->{{3.5679422440475245`*^9, 3.5679422965371246`*^9}, {
  3.567949268189625*^9, 3.567949315894325*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"A", "\[Rule]", 
     FractionBox[
      RowBox[{"pb", " ", "R"}], 
      RowBox[{
       RowBox[{"pa", " ", "pb"}], "+", 
       RowBox[{"3", " ", "pa", " ", "pn"}], "+", 
       RowBox[{"pb", " ", "pn"}]}]]}], ",", 
    RowBox[{"B1", "\[Rule]", 
     FractionBox[
      RowBox[{"pa", " ", "R"}], 
      RowBox[{
       RowBox[{"pa", " ", "pb"}], "+", 
       RowBox[{"3", " ", "pa", " ", "pn"}], "+", 
       RowBox[{"pb", " ", "pn"}]}]]}], ",", 
    RowBox[{"B2", "\[Rule]", 
     FractionBox[
      RowBox[{"pa", " ", "R"}], 
      RowBox[{
       RowBox[{"pa", " ", "pb"}], "+", 
       RowBox[{"3", " ", "pa", " ", "pn"}], "+", 
       RowBox[{"pb", " ", "pn"}]}]]}], ",", 
    RowBox[{"B3", "\[Rule]", 
     FractionBox[
      RowBox[{"pa", " ", "R"}], 
      RowBox[{
       RowBox[{"pa", " ", "pb"}], "+", 
       RowBox[{"3", " ", "pa", " ", "pn"}], "+", 
       RowBox[{"pb", " ", "pn"}]}]]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.567949316610325*^9}]
}, Open  ]]
},
WindowSize->{1064, 1825},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"6.0 for Microsoft Windows (64-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, 878, 27, 52, "Input"],
Cell[1471, 52, 650, 21, 47, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2158, 78, 1145, 34, 52, "Input"],
Cell[3306, 114, 811, 25, 47, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4154, 144, 1634, 46, 72, "Input"],
Cell[5791, 192, 1042, 32, 47, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)