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 Power

 http://functions.wolfram.com/01.02.06.0076.01

 Input Form

 1/(1 + z) == (1/z) Sum[(-1)^k/z^k, {k, 0, Infinity}] /; Abs[z] > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[FractionBox["1", RowBox[List["1", "+", "z"]]], "\[Equal]", RowBox[List[FractionBox["1", "z"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], SuperscriptBox["z", RowBox[List["-", "k"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]

 MathML Form

 1 1 + z 1 z k = 0 ( - 1 ) k z - k /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 Condition 1 1 z -1 1 z -1 k 0 -1 k z -1 k z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["1", RowBox[List["1", "+", "z_"]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["z", RowBox[List["-", "k"]]]]]]], "z"], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]]]

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

 2007-05-02