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 Tanh

 http://functions.wolfram.com/01.21.23.0001.01

 Input Form

 Sum[Tanh[a/2^k]/2^k, {k, 0, n}] == 2 Coth[2 a] - Coth[a/2^n]/2^n

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List["Tanh", "[", FractionBox["a", SuperscriptBox["2", "k"]], "]"]], SuperscriptBox["2", "k"]]]], "\[Equal]", RowBox[List[RowBox[List["2", " ", RowBox[List["Coth", "[", RowBox[List["2", " ", "a"]], "]"]]]], "-", FractionBox[RowBox[List["Coth", "[", FractionBox["a", SuperscriptBox["2", "n"]], "]"]], SuperscriptBox["2", "n"]]]]]]]]

 MathML Form

 k = 0 n 1 2 k tanh ( a 2 k ) 2 coth ( 2 a ) - 1 2 n coth ( a 2 n ) k 0 n 1 2 k -1 a 2 k -1 2 2 a -1 1 2 n -1 a 2 n -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "n_"], FractionBox[RowBox[List["Tanh", "[", FractionBox["a_", SuperscriptBox["2", "k_"]], "]"]], SuperscriptBox["2", "k_"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", RowBox[List["Coth", "[", RowBox[List["2", " ", "a"]], "]"]]]], "-", FractionBox[RowBox[List["Coth", "[", FractionBox["a", SuperscriptBox["2", "n"]], "]"]], SuperscriptBox["2", "n"]]]]]]]]

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

 2001-10-29