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http://functions.wolfram.com/04.11.25.0001.01
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Limit[Fibonacci[\[Nu]]/LucasL[\[Nu]], \[Nu] -> Infinity] == 1/Sqrt[5]
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Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["Fibonacci", "[", "\[Nu]", "]"]], RowBox[List["LucasL", "[", "\[Nu]", "]"]]], ",", RowBox[List["\[Nu]", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", FractionBox["1", SqrtBox["5"]]]]]]
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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> <mrow> <munder> <mi> lim </mi> <mrow> <mi> ν </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mfrac> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mi> ν </mi> </msub> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> ν </mi> </msub> </mfrac> </mrow> <mo>  </mo> <mfrac> <mn> 1 </mn> <msqrt> <mn> 5 </mn> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> ν </ci> </bvar> <condition> <apply> <tendsto /> <ci> ν </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <ci> Fibonacci </ci> <ci> ν </ci> </apply> <apply> <power /> <apply> <ci> LucasL </ci> <ci> ν </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["Fibonacci", "[", "\[Nu]_", "]"]], RowBox[List["LucasL", "[", "\[Nu]_", "]"]]], ",", RowBox[List["\[Nu]_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", SqrtBox["5"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
