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<b>let </b><font color="Maroon">seq</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>

<b>given </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><a NAME="E1:85"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">seq</font> <a href="comseq_3.html#K6" target="_self">^\</a> <font color="Maroon">n</font> is <a href="comseq_3.html#V1" target="_self">summable</a>
 ;<br/>

<a NAME="E2:85"/><i><font color="Green">E37</font></i>: 
(  <a href="comseq_3.html#K3" target="_self">Re</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_3.html#K6" target="_self">^\</a> <font color="Maroon">n</font></span>)</span> is <a href="series_1.html#V1">summable</a> &amp;  <a href="comseq_3.html#K4" target="_self">Im</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_3.html#K6" target="_self">^\</a> <font color="Maroon">n</font></span>)</span> is <a href="series_1.html#V1">summable</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:85"/>
(  <a href="comseq_3.html#K3" target="_self">Re</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_3.html#K6" target="_self">^\</a> <font color="Maroon">n</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">seq</font></span>)</span> <a href="seqm_3.html#K1">^\</a> <font color="Maroon">n</font> &amp;  <a href="comseq_3.html#K4" target="_self">Im</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_3.html#K6" target="_self">^\</a> <font color="Maroon">n</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">seq</font></span>)</span> <a href="seqm_3.html#K1">^\</a> <font color="Maroon">n</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:85"/><b>then </b>
(  <a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">seq</font> is <a href="series_1.html#V1">summable</a> &amp;  <a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">seq</font> is <a href="series_1.html#V1">summable</a> )
 
<b>by </b><i>, <a class="ref" href="series_1.html#T16">SERIES_1:16</a></i>;<br/>
<b>hence </b><a NAME="E5:85"/>
<font color="Maroon">seq</font> is <a href="comseq_3.html#V1" target="_self">summable</a>
 <b>by </b><i/>;<br/>


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