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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th27</font></span>: <a NAME="T28"><span class="comment"><font color="firebrick">:: LIOUVIL1:28</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">b</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp; <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="liouvil1.html#K3" title="LIOUVIL1:func.3">powerfact</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="newton.html#K7" title="NEWTON:func.7">!</a></span>)</span></span>)</span> <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Olive" title="b1">n</font></span>)</span></div></div>
