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http://functions.wolfram.com/01.07.23.0001.01
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Sum[Cos[a k], {k, 0, n}] == Csc[a/2] Sin[(1/2) a (n + 1)] Cos[(a n)/2]
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Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List["Cos", "[", RowBox[List["a", " ", "k"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Csc", "[", FractionBox["a", "2"], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "2"], " ", "a", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]], "]"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["a", " ", "n"]], "2"], "]"]]]]]]]]
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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> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <cos /> <apply> <times /> <ci> a </ci> <ci> k </ci> </apply> </apply> </apply> <apply> <times /> <apply> <csc /> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <ci> a </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <cos /> <apply> <times /> <ci> a </ci> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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_", "=", "0"]], "n_"], RowBox[List["Cos", "[", RowBox[List["a_", " ", "k_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Csc", "[", FractionBox["a", "2"], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "2"], " ", "a", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]], "]"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["a", " ", "n"]], "2"], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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