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<b>let </b><font color="Maroon" title="c2">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c3">s</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 ;<br/>

<a NAME="E2:30"/><b>then </b>
<font color="Maroon" title="c2">r</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c3">s</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 
<b>by </b><i><a class="ref" href="comseq_2.html#T17" target="_self" title="COMSEQ_2:th.17">Th17</a></i>;<br/>
<b>hence </b> <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="comseq_2.html#K1" title="COMSEQ_2:func.1">*'</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="ref" href="comseq_2.html#T12" target="_self" title="COMSEQ_2:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="txt" href="comseq_2.html#E1:30"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="comseq_2.html#T18" target="_self" title="COMSEQ_2:th.18">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T121" title="COMPLEX1:th.121">COMPLEX1:121</a></i>
;<br/><br/>


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