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 GoldenRatio

 http://functions.wolfram.com/02.02.23.0001.01

 Input Form

 Sum[Abs[Fibonacci[k] GoldenRatio - Fibonacci[k + 1]], {k, 1, Infinity}] == GoldenRatio

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["Abs", "[", RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "k", "]"]], " ", "GoldenRatio"]], "-", RowBox[List["Fibonacci", "[", RowBox[List["k", "+", "1"]], "]"]]]], "]"]]]], "\[Equal]", "GoldenRatio"]]]]

 MathML Form

 k = 1 "\[LeftBracketingBar]" F TagBox["F", Fibonacci] k ϕ TagBox["\[Phi]", Function[List[], GoldenRatio]] - F TagBox["F", Fibonacci] k + 1 "\[RightBracketingBar]" ϕ TagBox["\[Phi]", Function[List[], GoldenRatio]] k 1 Fibonacci k GoldenRatio -1 Fibonacci k 1 GoldenRatio [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], RowBox[List["Abs", "[", RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "k_", "]"]], " ", "GoldenRatio"]], "-", RowBox[List["Fibonacci", "[", RowBox[List["k_", "+", "1"]], "]"]]]], "]"]]]], "]"]], "\[RuleDelayed]", "GoldenRatio"]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02