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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E50">Th53</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: CATALAN2:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq1</font>, <font color="Olive" title="b2">seq2</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>  st <font color="Olive" title="b1">seq1</font> is  <a href="series_1.html#V2" title="SERIES_1:attr.2">absolutely_summable</a>  &amp; <font color="Olive" title="b2">seq2</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  holds <br/>( <font color="Olive" title="b1">seq1</font> <a href="catalan2.html#K4" title="CATALAN2:func.4">(##)</a> <font color="Olive" title="b2">seq2</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  &amp;  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">seq1</font> <a href="catalan2.html#K4" title="CATALAN2:func.4">(##)</a> <font color="Olive" title="b2">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <font color="Olive" title="b1">seq1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <font color="Olive" title="b2">seq2</font></span>)</span> )</div></div>
