Limit[LucasL[\[Nu]]/Fibonacci[\[Nu]], \[Nu] -> Infinity] == Sqrt[5]

Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["LucasL", "[", "\[Nu]", "]"]], RowBox[List["Fibonacci", "[", "\[Nu]", "]"]]], ",", RowBox[List["\[Nu]", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", SqrtBox["5"]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> &#957; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mfrac> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox[&quot;L&quot;, LucasL] </annotation> </semantics> <mi> &#957; </mi> </msub> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox[&quot;F&quot;, Fibonacci] </annotation> </semantics> <mi> &#957; </mi> </msub> </mfrac> </mrow> <mo> &#63449; </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> &#957; </ci> </bvar> <condition> <apply> <tendsto /> <ci> &#957; </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <ci> LucasL </ci> <ci> &#957; </ci> </apply> <apply> <power /> <apply> <ci> Fibonacci </ci> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["LucasL", "[", "\[Nu]_", "]"]], RowBox[List["Fibonacci", "[", "\[Nu]_", "]"]]], ",", RowBox[List["\[Nu]_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox["5"]]]]]

2007-05-02