8.4

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#006666" TEXT="#080000"> <div> <B>C á l c u l o  2 1</B><FONT SIZE="4" COLOR="#FFFFCC" FACE="Bell MT" >   </FONT><B>  | </B>  <A HREF="index.htm" TARGET="_top" TITLE="Cálculo 21"><U>Home</U></A>  |  <A HREF="id98.htm" TARGET="_top" TITLE="Contenido"><U>Contenido</U></A>  | <A HREF="id488.htm" TARGET="_top" TITLE="Leithold EC7"><U>Leithold</U></A> </div> <bR> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Ejercicios 8.4</div> <div> <B>Series infinitas de términos positivos</B></div> <bR> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3926688482" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B> <A NAME="criterio_de_comparación"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>Criterio de comparación</B></div> <div> <B><IMG SRC="274fba330.gif" border=0 width="442" height="307" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="criterio_de_comparación_del_paso_al"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>Criterio de comparación del paso al límite</B></div> <div> <B><IMG SRC="2750d1d50.gif" border=0 width="465" height="213" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="criterio_de_la_integral"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>Criterio de la integral</B></div> <div> <B><IMG SRC="275adec30.gif" border=0 width="478" height="195" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >1</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >24</FONT>, determine si la serie es convergente o divergente aplicando el <A HREF="#criterio_de_comparación" TITLE="8.4"><U>criterio de comparación</U></A> o el <A HREF="#criterio_de_comparación_del_paso_al" TITLE="8.4"><U>criterio de comparación por paso al límite</U></A>.</div> <div> <FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="27524b300.gif" border=0 width="75" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#1" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="275443300.gif" border=0 width="67" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#3" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="275665310.gif" border=0 width="101" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#6" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="27586d310.gif" border=0 width="109" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#9" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >25</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >32</FONT>, aplique el <A HREF="#criterio_de_la_integral" TITLE="8.4"><U>criterio de la integral</U></A> para determinar si la serie es convergente o divergente.</div> <div> <FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="275c78330.gif" border=0 width="120" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#27" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="275e7d390.gif" border=0 width="125" height="57" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#30" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      </div> <div> <FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >33</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >48</FONT>, utilice cualquier método para determinar si la serie es convergente o divergente:</div> <div>  <IMG SRC="276654300.gif" border=0 width="84" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#33" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="27675f300.gif" border=0 width="95" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#36" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="276854300.gif" border=0 width="84" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#39" TITLE="8.4"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <DIV ALIGN="LEFT"></DIV> <div> <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >Soluciones</FONT></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="2751c0500.gif" border=0 width="704" height="336" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="2753c56b0.gif" border=0 width="709" height="363" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="2755bb850.gif" border=0 width="699" height="389" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <IMG SRC="2757bb700.gif" border=0 width="699" height="368" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="27"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>27</div> <div> <IMG SRC="275b417c0.gif" border=0 width="577" height="380" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="30"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>30</div> <div> <IMG SRC="275d6cfc0.gif" border=0 width="620" height="508" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="33"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>33</div> <div> <IMG SRC="275f10430.gif" border=0 width="784" height="323" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="36"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>36</div> <div> <IMG SRC="276268430.gif" border=0 width="616" height="323" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="39"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>39</div> <div> <IMG SRC="2764c0650.gif" border=0 width="704" height="357" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </td> <td valign="top" rowspan="2" width=105 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <A HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><B><IMG SRC="2c0564580.gif" border=0 width="100" height="600" ALIGN="BOTTOM" HSPACE="0" 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