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 Binomial

 http://functions.wolfram.com/06.03.23.0004.01

 Input Form

 Sum[Binomial[n, k] k, {k, 0, Infinity}] == 2^(n - 1) n

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], " ", "k"]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List["n", "-", "1"]]], " ", "n"]]]]]]

 MathML Form

 k = 0 ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] k 2 n - 1 n k 0 Binomial n k k 2 n -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n_", ",", "k_"]], "]"]], " ", "k_"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["n", "-", "1"]]], " ", "n"]]]]]]

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

 2001-10-29