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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: LP_SPACE:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b3">p</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">p</font> &amp; <font color="Olive" title="b1">a</font> <a href="lp_space.html#K1" title="LP_SPACE:func.1">rto_power</a> <font color="Olive" title="b3">p</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  &amp; <font color="Olive" title="b2">b</font> <a href="lp_space.html#K1" title="LP_SPACE:func.1">rto_power</a> <font color="Olive" title="b3">p</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="lp_space.html#K1" title="LP_SPACE:func.1">rto_power</a> <font color="Olive" title="b3">p</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  &amp; <span class="p1">(<span class="default"><a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="lp_space.html#K1" title="LP_SPACE:func.1">rto_power</a> <font color="Olive" title="b3">p</font></span>)</span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lp_space.html#K1" title="LP_SPACE:func.1">rto_power</a> <font color="Olive" title="b3">p</font></span>)</span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b3">p</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">b</font> <a href="lp_space.html#K1" title="LP_SPACE:func.1">rto_power</a> <font color="Olive" title="b3">p</font></span>)</span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b3">p</font></span>)</span></span>)</span> )</div></div>
