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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>thus </b><a href="irrat_1.html#K5" target="_self">eseq</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font> = 
1 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K12">!</a> </span>)</span>
<b>by </b><i><a class="ref" href="irrat_1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="newton.html#K3">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K12">!</a> </span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T15">NEWTON:15</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="sin_cos.html#K7">ExpSeq</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="sin_cos.html#D9">SIN_COS:def 9</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E2:31"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="irrat_1.html#K5" target="_self">eseq</a>  <a href="hidden.html#R1">=</a> 1 <a href="sin_cos.html#K7">ExpSeq</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>
<b>hence </b><a NAME="E3:31"/>
 <a href="irrat_1.html#K5" target="_self">eseq</a>  is <a href="series_1.html#V1">summable</a>
 <b>by </b><i><a class="ref" href="sin_cos.html#T49">SIN_COS:49</a></i>;<br/>

<b>thus </b> <a href="sin_cos.html#K29">exp_R</a> 1 = 
<a href="sin_cos.html#K27">exp_R</a>  <a href="seq_1.html#K2">.</a> 1
<b>by </b><i><a class="ref" href="sin_cos.html#D27">SIN_COS:def 27</a></i>
<br/>.= 
 <a href="series_1.html#K2">Sum</a> <a href="irrat_1.html#K5" target="_self">eseq</a> 
<b>by </b><i><a class="txt" href="irrat_1.html#E2:31"><i><font color="Green">E29</font></i></a>, <a class="ref" href="sin_cos.html#D26">SIN_COS:def 26</a></i>
;<br/>


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