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http://functions.wolfram.com/06.03.23.0041.01
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Sum[k^11/(2^k Binomial[2 k, k]), {k, 1, Infinity}] ==
5724192868004/282475249 + (12522296655976 ArcCot[Sqrt[7]])/
(282475249 Sqrt[7])
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Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["-", "k"]]], " ", SuperscriptBox["k", "11"]]], RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "k"]], ",", "k"]], "]"]]]]], "\[Equal]", RowBox[List[FractionBox["5724192868004", "282475249"], "+", FractionBox[RowBox[List["12522296655976", " ", RowBox[List["ArcCot", "[", SqrtBox["7"], "]"]]]], RowBox[List["282475249", " ", SqrtBox["7"]]]]]]]]]]
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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> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mfrac> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> k </mi> <mn> 11 </mn> </msup> </mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["2", " ", "k"]], Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> </mfrac> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 5724192868004 </mn> <mn> 282475249 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 12522296655976 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mn> 7 </mn> </msqrt> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 282475249 </mn> <mo> ⁢ </mo> <msqrt> <mn> 7 </mn> </msqrt> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <power /> <ci> k </ci> <cn type='integer'> 11 </cn> </apply> <apply> <power /> <apply> <ci> Binomial </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='rational'> 5724192868004 <sep /> 282475249 </cn> <apply> <times /> <cn type='integer'> 12522296655976 </cn> <apply> <arccot /> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 282475249 </cn> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["-", "k_"]]], " ", SuperscriptBox["k_", "11"]]], RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "k_"]], ",", "k_"]], "]"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["5724192868004", "282475249"], "+", FractionBox[RowBox[List["12522296655976", " ", RowBox[List["ArcCot", "[", SqrtBox["7"], "]"]]]], RowBox[List["282475249", " ", SqrtBox["7"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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