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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:22"/>
<font color="Maroon">seq</font> <a href="seqm_3.html#K1">^\</a> 1 is <a href="series_1.html#V1">summable</a>
 ;<br/>

<b>hence </b><a NAME="E2:22"/>
<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 href="series_1.html#K2">Sum</a> <font color="Maroon">seq</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K2">.</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="series_1.html#K2">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="seqm_3.html#K1">^\</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="series_1.html#T18">SERIES_1:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="series_1.html#K2">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="series_1.html#D1">SERIES_1:def 1</a></i>
;<br/><br/>


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