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 Floor

 http://functions.wolfram.com/04.01.21.0004.01

 Input Form

 Integrate[Floor[t], {t, 0, n}] == (n (n - 1))/2 /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "n"], RowBox[List[RowBox[List["Floor", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", FractionBox[RowBox[List["n", RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]]]], "2"]]], " ", "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["n", ",", "Integers"]], "]"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 0 n t t n ( n - 1 ) 2 /; n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] Condition t 0 n t n n -1 2 -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "n_"], RowBox[List[RowBox[List["Floor", "[", "t_", "]"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "n", " ", RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29