Pi/2 == 1 - 1/(3 - 6/(1 - 2/(3 - 20/(1 - 12/(3 - 42/(1 - 30/(3 - \[Ellipsis])))))))

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> - </mo> <mfrac> <mn> 6 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 2 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> - </mo> <mfrac> <mn> 20 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 12 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> - </mo> <mfrac> <mn> 42 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 30 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> - </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 42 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#8230; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["\[Pi]", "2"], "]"]], "\[RuleDelayed]", RowBox[List["1", "-", FractionBox["1", RowBox[List["3", "-", FractionBox["6", RowBox[List["1", "-", FractionBox["2", RowBox[List["3", "-", FractionBox["20", RowBox[List["1", "-", FractionBox["12", RowBox[List["3", "-", FractionBox["42", RowBox[List["1", "-", FractionBox["30", RowBox[List["3", "-", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]]]]

2001-10-29