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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/>



<b>assume </b><a NAME="E1:56"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="comseq_2.html#V1" target="_self">bounded</a> &amp;  <a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K5">0c</a>  )
 ;<br/>

<a NAME="E2:56"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a>
 
<b>by </b><i><a class="ref" href="comseq_2.html#T42" target="_self">Th42</a></i>;<br/>
<b>hence </b> <a href="seq_2.html#K2">lim</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> = 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="comseq_2.html#T11" target="_self">Th11</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="comseq_2.html#E1:56"><i><font color="Green">E31</font></i></a>, <a class="ref" href="comseq_2.html#T43" target="_self">Th43</a>, <a class="ref" href="complex1.html#T130">COMPLEX1:130</a></i>
;<br/><br/>


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