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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E37">Th31</font></span>: <a NAME="T33"><span class="comment"><font color="firebrick">:: LIOUVIL1:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font> being   <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b2">b</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp;  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b1">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">b</font> holds <br/> <a href="liouvil1.html#K4" title="LIOUVIL1:func.4">Liouville_seq</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a> </div></div>
