<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T46"><span class="comment"><font color="firebrick">:: SUPINF_2:46</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a>  st <font color="Olive" title="b1">F</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>  &amp;  ex <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <font color="Olive" title="b1">F</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  holds <br/> not <font color="Olive" title="b1">F</font> is  <a href="supinf_2.html#V7" title="SUPINF_2:attr.7">summable</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="supinf_2.html#T45" target="_self" onmouseover="rs('supinf_2/T45')" onmouseout="rh()">Th44</a></span>;<br/></div></div>
