<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:42"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<b>assume </b><a NAME="E2:42"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K4" target="_self">-Root</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:42"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E1:42"><i><font color="Green">E34</font></i></a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="seq_1.html#NM1">Real_Sequence</a><b> such that </b><br/><a NAME="E5:42"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="seq_1.html#S1">SEQ_1:sch 1</a>();<br/></i>
<a NAME="E6:42"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="prepower.html#E5:42"><i><font color="Green">E37</font></i></a>, <a class="ref" href="seq_4.html#T46">SEQ_4:46</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> 1 as   <a href="seq_1.html#NM1">Real_Sequence</a> <b>by </b><i><a class="ref" href="funcop_1.html#T57">FUNCOP_1:57</a></i>;<br/>
<a NAME="E8:42"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E9:42"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="ref" href="seq_4.html#T39">SEQ_4:39</a></i>;<br/>
<a NAME="E10:42"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="txt" href="prepower.html#E6:42"><i><font color="Green">E38</font></i></a>, <a class="ref" href="seq_2.html#T19">SEQ_2:19</a></i>;<br/>
<i><font color="Green">E42</font></i>:  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> 0</span>)</span> <a href="real_1.html#K3">+</a> 0
<b>by </b><i><a class="txt" href="prepower.html#E6:42"><i><font color="Green">E38</font></i></a>, <a class="ref" href="seq_4.html#T59">SEQ_4:59</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="prepower.html#E8:42"><i><font color="Green">E39</font></i></a></i>
;<br/>
<i><font color="Green">E43</font></i>:  <a href="seq_2.html#K2">lim</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> 0
<b>by </b><i><a class="ref" href="seq_4.html#T41">SEQ_4:41</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="prepower.html#E8:42"><i><font color="Green">E39</font></i></a></i>
;<br/>
<div><i><font color="Green">E44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:42_3"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><i><font color="Green">E46</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="seqm_3.html#D9">SEQM_3:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="prepower.html#E2:42"><i><font color="Green">E35</font></i></a>, <a class="txt" href="prepower.html#E1:42_3"><i><font color="Green">E45</font></i></a></i>
;<br/><a NAME="E3:42_3"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="prepower.html#E1:42"><i><font color="Green">E34</font></i></a>, <a class="txt" href="prepower.html#E1:42_3"><i><font color="Green">E45</font></i></a>, <a class="ref" href="prepower.html#T38" target="_self">Th38</a></i>;<br/><a NAME="E4:42_3"/><b>then </b><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1;<br/><a NAME="E5:42_3"/><i><font color="Green">E49</font></i>: 
 <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="prepower.html#E4:42_3"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E6:42_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="prepower.html#K3" target="_self">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="prepower.html#E3:42"><i><font color="Green">E36</font></i></a>, <a class="txt" href="prepower.html#E1:42_3"><i><font color="Green">E45</font></i></a>, <a class="txt" href="prepower.html#E2:42_3"><i><font color="Green">E46</font></i></a>, <a class="txt" href="prepower.html#E33"><i><font color="Green">Lemma20</font></i></a></i>;<br/><a NAME="E7:42_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="prepower.html#E5:42_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="prepower.html#T24" target="_self">Th24</a></i>;<br/><a NAME="E8:42_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E9:42_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E10:42_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>
 ;<br/><a NAME="E11:42_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/><a NAME="E12:42_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>;<br/><a NAME="E13:42_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E14:42_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="prepower.html#E8:42"><i><font color="Green">E39</font></i></a></i>;<br/><a NAME="E15:42_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="prepower.html#E5:42"><i><font color="Green">E37</font></i></a></i>;<br/><b>hence </b><a NAME="E16:42_3"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="prepower.html#E8:42"><i><font color="Green">E39</font></i></a>, <a class="txt" href="prepower.html#E3:42_3"><i><font color="Green">E47</font></i></a>, <a class="ref" href="seq_1.html#T11">SEQ_1:11</a></i>;<br/></div><b>end;</b></div>
<a NAME="E14:42"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1 is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="txt" href="prepower.html#E9:42"><i><font color="Green">E40</font></i></a>, <a class="txt" href="prepower.html#E10:42"><i><font color="Green">E41</font></i></a>, <a class="txt" href="prepower.html#E11:42"><i><font color="Green">E42</font></i></a>, <a class="txt" href="prepower.html#E12:42"><i><font color="Green">E43</font></i></a>, <a class="ref" href="seq_2.html#T33">SEQ_2:33</a></i>;<br/>
<a NAME="E15:42"/><i><font color="Green">E46</font></i>: 
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E9:42"><i><font color="Green">E40</font></i></a>, <a class="txt" href="prepower.html#E10:42"><i><font color="Green">E41</font></i></a>, <a class="txt" href="prepower.html#E11:42"><i><font color="Green">E42</font></i></a>, <a class="txt" href="prepower.html#E12:42"><i><font color="Green">E43</font></i></a>, <a class="txt" href="prepower.html#E13:42"><i><font color="Green">E44</font></i></a>, <a class="ref" href="seq_2.html#T34">SEQ_2:34</a></i>;<br/>
<b>thus </b><a NAME="E16:42"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V4">convergent</a>
 <b>by </b><i><a class="txt" href="prepower.html#E14:42"><i><font color="Green">E45</font></i></a>, <a class="ref" href="seq_4.html#T35">SEQ_4:35</a></i>;<br/>

<b>thus </b><a NAME="E17:42"/>
 <a href="seq_2.html#K2">lim</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="prepower.html#E14:42"><i><font color="Green">E45</font></i></a>, <a class="txt" href="prepower.html#E15:42"><i><font color="Green">E46</font></i></a>, <a class="ref" href="seq_4.html#T36">SEQ_4:36</a></i>;<br/>


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