ag-gipp/GoUldI

{
  "definitions" : {
    "k" : [ {
      "Q21199" : "natural number (numbers used for counting and ordering)"
    } ],
    "n" : [ {
      "Q21199" : "natural number (numbers used for counting and ordering)"
    } ]
  },
  "constraints" : [ "1\\leq k\\leq n-1," ],
  "math_inputtex" : "(1+2+\\ldots+k+\\ldots+(n-1))",
  "math_inputtex_semantic" : "(1+2+\\ldots+\\w{Q21199}{k}+\\ldots+(\\w{Q21199}{n}-1))",
  "correct_tex" : "(1+2+\\ldots+k+\\ldots+(n-1))",
  "correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"(1+2+\\ldots+k+\\ldots+(n-1))\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.18\" xref=\"p1.1.m1.1.18.2.cmml\">\n      <mo stretchy=\"false\" id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.18.2.cmml\">(</mo>\n      <mrow id=\"p1.1.m1.1.18.2\" xref=\"p1.1.m1.1.18.2.cmml\">\n        <mn id=\"p1.1.m1.1.2\" xref=\"p1.1.m1.1.2.cmml\">1</mn>\n        <mo id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">+</mo>\n        <mn id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.4.cmml\">2</mn>\n        <mo id=\"p1.1.m1.1.3a\" xref=\"p1.1.m1.1.3.cmml\">+</mo>\n        <mi mathvariant=\"normal\" id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.6.cmml\">…</mi>\n        <mo id=\"p1.1.m1.1.3b\" xref=\"p1.1.m1.1.3.cmml\">+</mo>\n        <mi id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.8.cmml\">k</mi>\n        <mo id=\"p1.1.m1.1.3c\" xref=\"p1.1.m1.1.3.cmml\">+</mo>\n        <mi mathvariant=\"normal\" id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">…</mi>\n        <mo id=\"p1.1.m1.1.3d\" xref=\"p1.1.m1.1.3.cmml\">+</mo>\n        <mrow id=\"p1.1.m1.1.18.2.1\" xref=\"p1.1.m1.1.18.2.1.2.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.12\" xref=\"p1.1.m1.1.18.2.1.2.cmml\">(</mo>\n          <mrow id=\"p1.1.m1.1.18.2.1.2\" xref=\"p1.1.m1.1.18.2.1.2.cmml\">\n            <mi id=\"p1.1.m1.1.13\" xref=\"p1.1.m1.1.13.cmml\">n</mi>\n            <mo id=\"p1.1.m1.1.14\" xref=\"p1.1.m1.1.14.cmml\">-</mo>\n            <mn id=\"p1.1.m1.1.15\" xref=\"p1.1.m1.1.15.cmml\">1</mn>\n          </mrow>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.16\" xref=\"p1.1.m1.1.18.2.1.2.cmml\">)</mo>\n        </mrow>\n      </mrow>\n      <mo stretchy=\"false\" id=\"p1.1.m1.1.17\" xref=\"p1.1.m1.1.18.2.cmml\">)</mo>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.18.2.cmml\" xref=\"p1.1.m1.1.18\">\n        <plus id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\"/>\n        <cn type=\"integer\" id=\"p1.1.m1.1.2.cmml\" xref=\"p1.1.m1.1.2\">1</cn>\n        <cn type=\"integer\" id=\"p1.1.m1.1.4.cmml\" xref=\"p1.1.m1.1.4\">2</cn>\n        <ci id=\"p1.1.m1.1.6.cmml\" xref=\"p1.1.m1.1.6\">…</ci>\n        <csymbol cd=\"latexml\" id=\"p1.1.m1.1.8.cmml\" xref=\"p1.1.m1.1.8\">Q21199</csymbol>\n        <ci id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\">…</ci>\n        <apply id=\"p1.1.m1.1.18.2.1.2.cmml\" xref=\"p1.1.m1.1.18.2.1\">\n          <minus id=\"p1.1.m1.1.14.cmml\" xref=\"p1.1.m1.1.14\"/>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.13.cmml\" xref=\"p1.1.m1.1.13\">Q21199</csymbol>\n          <cn type=\"integer\" id=\"p1.1.m1.1.15.cmml\" xref=\"p1.1.m1.1.15\">1</cn>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">(1+2+\\ldots+k+\\ldots+(n-1))</annotation>\n  </semantics>\n</math>",
  "uri" : "https://arxiv.org/abs/0904.3855",
  "title" : "Arithmetic Progression",
  "comment" : "",
  "type" : "general formula",
  "ntcir12-type" : "3",
  "formula" : "1_220.496",
  "page" : "44",
  "ntcir12-relevance" : "4"
}