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<div><span class="kw">theorem </span><a NAME="T34"><span class="comment"><font color="firebrick">:: LOPBAN_3:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">p</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp; (  for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/><span class="p1"><a href="normsp_0.html#K5" title="NORMSP_0:func.5">||.</a><span class="default"><font color="Olive" title="b2">seq</font></span><a href="normsp_0.html#K5" title="NORMSP_0:func.5">.||</a></span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b3">p</font></span>)</span> ) holds <br/><font color="Olive" title="b2">seq</font> is  <a href="lopban_3.html#V2" title="LOPBAN_3:attr.2">norm_summable</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="series_1.html#T32" onmouseover="rs('series_1/T32')" onmouseout="rh()">SERIES_1:32</a></span>;<br/></div></div>
