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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<i><font color="Green">E24</font></i>:  <a href="comseq_3.html#K3" target="_self">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K2">+</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T15" target="_self">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T26" target="_self">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T26" target="_self">Th26</a></i>
<br/>.= 
 <a href="series_1.html#K1">Partial_Sums</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="series_1.html#T8">SERIES_1:8</a></i>
<br/>.= 
 <a href="series_1.html#K1">Partial_Sums</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T15" target="_self">Th15</a></i>
<br/>.= 
 <a href="comseq_3.html#K3" target="_self">Re</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T26" target="_self">Th26</a></i>
;<br/>
 <a href="comseq_3.html#K4" target="_self">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K2">+</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T15" target="_self">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T26" target="_self">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T26" target="_self">Th26</a></i>
<br/>.= 
 <a href="series_1.html#K1">Partial_Sums</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="series_1.html#T8">SERIES_1:8</a></i>
<br/>.= 
 <a href="series_1.html#K1">Partial_Sums</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T15" target="_self">Th15</a></i>
<br/>.= 
 <a href="comseq_3.html#K4" target="_self">Im</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_3.html#T26" target="_self">Th26</a></i>
;<br/>
<b>hence </b><a NAME="E3:38"/>
<span class="p1">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="comseq_3.html#K7" target="_self">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="comseq_3.html#E1:38"><i><font color="Green">E24</font></i></a>, <a class="ref" href="comseq_3.html#T14" target="_self">Th14</a></i>;<br/>


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