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 | | http://functions.wolfram.com/06.03.23.0031.01 | 
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 | | Sum[k/(2^k Binomial[2 k, k]), {k, 1, Infinity}] == 
 12/49 + (40 ArcCot[Sqrt[7]])/(49 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"]]], " ", "k"]], RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "k"]], ",", "k"]], "]"]]]]], "\[Equal]", RowBox[List[FractionBox["12", "49"], "+", FractionBox[RowBox[List["40", " ", RowBox[List["ArcCot", "[", SqrtBox["7"], "]"]]]], RowBox[List["49", " ", 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>  <mi> k </mi>  </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> 12 </mn>  <mn> 49 </mn>  </mfrac>  <mo> + </mo>  <mfrac>  <mrow>  <mn> 40 </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> 49 </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>  <ci> k </ci>  <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'> 12 <sep /> 49 </cn>  <apply>  <times />  <cn type='integer'> 40 </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'> 49 </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_"]]], " ", "k_"]], RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "k_"]], ",", "k_"]], "]"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["12", "49"], "+", FractionBox[RowBox[List["40", " ", RowBox[List["ArcCot", "[", SqrtBox["7"], "]"]]]], RowBox[List["49", " ", SqrtBox["7"]]]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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