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<b>let </b><font color="Maroon">X</font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:50"/>
( ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   holds <span class="p1"><a href="clvect_1.html#K10">||.</a><span class="default"><font color="Maroon">seq</font></span><a href="clvect_1.html#K10">.||</a></span> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) &amp;  ex <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">m</font> holds <br/><span class="p1">(<span class="default"><span class="p2"><a href="clvect_1.html#K10">||.</a><span class="default"><font color="Maroon">seq</font></span><a href="clvect_1.html#K10">.||</a></span> <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="clvect_1.html#K10">||.</a><span class="default"><font color="Maroon">seq</font></span><a href="clvect_1.html#K10">.||</a></span> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 ;<br/>

<b>hence </b><a NAME="E2:50"/>
not <span class="p1"><a href="clvect_1.html#K10">||.</a><span class="default"><font color="Maroon">seq</font></span><a href="clvect_1.html#K10">.||</a></span> is <a href="series_1.html#V1">summable</a>
 <b>by </b><i><a class="ref" href="series_1.html#T31">SERIES_1:31</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="clopban3.html#D4" target="_self">CLOPBAN3:def 4</a><br/>


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