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  <region id="0" left="45" top="27" width="234" height="24" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>what does the summatory now</p>
    </text>
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        <e type="operand">n</e>
        <e type="operand">5</e>
        <e type="operator" args="2">←</e>
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        <e type="operand">A</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="function" args="2">matrix</e>
        <e type="operator" args="2">←</e>
      </input>
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  <region id="3" left="45" top="108" width="182" height="81" color="#000000" background-color="#ffffff" font-size="10">
    <math fraction-type="none" optimize="1" error="9">
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        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operator" args="2">←</e>
        <e type="operand">i</e>
        <e type="operand">5</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">i</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">←</e>
        <e type="operand">A</e>
        <e type="operand">i</e>
        <e type="function" args="2">el</e>
        <e type="operand">j</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="function" args="4">sum</e>
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    <math optimize="1">
      <input>
        <e type="operand">A</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" args="7">mat</e>
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    <math fraction-type="none" optimize="1">
      <input>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="operand">6</e>
        <e type="operand">10</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" args="7">mat</e>
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  <region id="6" left="189" top="225" width="188" height="24" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>the expected value is </p>
    </text>
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    <math optimize="1" error="68">
      <input>
        <e type="operand">k</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="function" args="4">sum</e>
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      <result action="numeric">
        <e type="operand">#</e>
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  <region id="8" left="180" top="306" width="176" height="24" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>this is the problem!</p>
    </text>
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  <region id="9" left="45" top="360" width="89" height="63" color="#000000" background-color="#ffffff" font-size="10">
    <math optimize="1">
      <input>
        <e type="operand">k</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" args="4">sum</e>
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      <result action="numeric">
        <e type="operand">1</e>
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  <region id="10" left="180" top="378" width="265" height="24" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>from here, there is no problem!</p>
    </text>
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  <region id="11" left="36" top="432" width="724" height="24" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>the improvement that you introduced would be doing two iterations in these cases, isnt?</p>
    </text>
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  <region id="12" left="54" top="468" width="89" height="63" color="#000000" background-color="#ffffff" font-size="10">
    <math optimize="1">
      <input>
        <e type="operand">k</e>
        <e type="operand">k</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="function" args="4">sum</e>
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      <result action="numeric">
        <e type="operand">5</e>
      </result>
    </math>
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  <region id="13" left="261" top="468" width="77" height="63" color="#000000" background-color="#ffffff" font-size="10">
    <math optimize="1">
      <input>
        <e type="operand">k</e>
        <e type="operand">k</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" args="4">sum</e>
        <e type="operand">5</e>
        <e type="operator" args="2">≡</e>
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  <region id="14" left="36" top="540" width="955" height="24" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>in the second one,we only need to have a zero result, because no iteration will happen from 3 to 2 if going forward </p>
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  <region id="15" left="36" top="585" width="536" height="24" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>A great solution would be something like "forcing" the notation:</p>
    </text>
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  <region id="18" left="135" top="702" width="176" height="72" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>this is incompatiblewith going forward,so the result is 0, but not an error</p>
    </text>
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  <region id="19" left="324" top="702" width="176" height="56" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="spa">
      <p>this is compatiblewith going backward,so the result is 5</p>
    </text>
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