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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>





<b>assume </b><a NAME="E1:53"/><i><font color="Green">E38</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="power.html#K2">-root</a> <span class="p1">(<span class="default"><span class="p2"><a href="clvect_1.html#K10">||.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="clvect_1.html#K10">.||</a></span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 ;<br/>

<a NAME="E2:53"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1"><a href="clvect_1.html#K10">||.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="clvect_1.html#K10">.||</a></span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="clopban3.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E3:53"/>
not <span class="p1"><a href="clvect_1.html#K10">||.</a><span class="default"><font color="Maroon">c<sub>2</sub></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="txt" href="clopban3.html#E1:53"><i><font color="Green">E38</font></i></a>, <a class="ref" href="series_1.html#T34">SERIES_1:34</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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