9.2

<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" ><B>   </B></FONT><B>  | </B>  <A HREF="index.htm" TARGET="_top" TITLE="Cálculo 21"><U><B>Home</B></U></A><B>  |  </B><A HREF="id98.htm" TARGET="_top" TITLE="Contenido"><U><B>Contenido</B></U></A><B>  |  </B><A HREF="id504.htm" TARGET="_top" TITLE="Larson y Edwards"><U><B>Larson y Edwards</B></U></A><B> </B></div> <div> </div> </td> </tr><tr> <td valign="top" width=160 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Series infinitas</div> <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=456 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>Ejercicios 9.2</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>Series y convergencia</B></div> <div>  <A NAME="definición_de_serie_infinita"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Definición de serie infinita</div> <div> <B>Definición de serie infinita</B></div> <div> <B><IMG SRC="2b78b57d0.gif" border=0 width="693" height="125" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="2b79f0190.gif" border=0 width="496" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >.</FONT></div> <div>  <A NAME="definición_de_serie_convergente_y"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Definición de serie convergente y divergente</div> <div> <B>Definición de serie convergente y divergente</B></div> <div> <B><IMG SRC="2b7c17e70.gif" border=0 width="791" height="231" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="serie_telescópica"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Serie telescópica</div> <div> <B>Serie telescópica</B></div> <div> Una serie telescópica es de la forma</div> <DIV ALIGN="LEFT"></DIV> <div> <B><IMG SRC="2b7d70210.gif" border=0 width="368" height="33" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> La suma parcial <I>n</I>-ésima de una serie telescópica es </div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="2b7e6d1d0.gif" border=0 width="109" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="2b7f0b230.gif" border=0 width="779" height="35" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> La suma de una serie telescópica convergente está dada por</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="2b8089230.gif" border=0 width="137" height="35" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="serie_geometrica"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>serie geometrica</div> <div> <B>Serie geométrica</B></div> <div> Una serie geométrica de razón <I><B>r</B></I> y con primer término <FONT SIZE="4" COLOR="#003333" FACE="Times New Roman" ><I>a</I></FONT> está dada por </div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="2b8153330.gif" border=0 width="339" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <B>Teorema. Convergencia y suma de una serie geométrica</B></div> <div> <B><IMG SRC="2b8253510.gif" border=0 width="851" height="81" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="propiedades_de_series_infinitas"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Propiedades de series infinitas</div> <div> <B>Propiedades de las series infinitas</B></div> <div> <B><IMG SRC="2b83e56c0.gif" border=0 width="741" height="108" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="criterio_para_la_divergencia"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Criterio para la divergencia</div> <div> <B>Teorema. Límite del término n-ésimo de una serie convergente</B></div> <div> <B><IMG SRC="2b8450330.gif" border=0 width="336" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <IMG BORDER="0" SRC="Symb075c00b7014033993300.gif" HEIGHT="21" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">E<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >l contrarecíproco del teorema anterior proporciona un criterio para determinar si una serie es divergente:</FONT></div> <div> <B>Teorema. Criterio del término n-ésimo para la divergencia</B></div> <div> <B><IMG SRC="2ba03f330.gif" border=0 width="319" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <DIV ALIGN="LEFT"></DIV> <div>  <A NAME="enunciados"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Enunciados</div> <div> <B>Enunciados de los ejercicios</B></div> <bR> <div> <FONT SIZE="4" COLOR="#006699" FACE="Bell MT" ><B>E</B></FONT>n los ejercicios <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >1</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >6</FONT>, encontrar los primeros cinco términos de la sucesión de las sumas parciales <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >1</FONT>, <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >2</FONT>, <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >3</FONT>, <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >4</FONT><FONT SIZE="1" COLOR="#000000" FACE="Bell MT" > </FONT>y <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >5</FONT>.</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="2b6ed02c0.gif" border=0 width="208" height="44" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#1" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b87232c0.gif" border=0 width="291" height="44" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#2" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b89e82c0.gif" border=0 width="232" height="44" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#3" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="2b8be52c0.gif" border=0 width="229" height="44" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#4" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b8d5c370.gif" border=0 width="92" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#5" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b8f743d0.gif" border=0 width="116" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#6" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> <FONT SIZE="4" COLOR="#006699" FACE="Bell MT" ><B>E</B></FONT>n los ejercicios <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >7</FONT> y <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >8</FONT>, determinar si <IMG SRC="2b90651f0.gif" border=0 width="101" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> son convergentes.</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="2b92692c0.gif" border=0 width="105" height="44" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#7" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b9475350.gif" border=0 width="117" height="53" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#8" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> <FONT SIZE="4" COLOR="#006699" FACE="Bell MT" ><B>E</B></FONT>n los ejercicios <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >9</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >18</FONT>, verificar que la serie infinita diverge.</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="2b9763390.gif" border=0 width="99" height="57" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#9" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b9a7f390.gif" border=0 width="127" height="57" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#10" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b9cb1370.gif" border=0 width="177" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#11" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2b9e97370.gif" border=0 width="151" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#12" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2ba167370.gif" border=0 width="103" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#13" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="2ba373370.gif" border=0 width="115" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#14" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2ba56d370.gif" border=0 width="109" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#15" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <B><IMG SRC="2ba77f370.gif" border=0 width="127" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="#16" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2ba96f370.gif" border=0 width="111" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#17" TITLE="9.2"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="2bab58370.gif" border=0 width="88" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#18" TITLE="9.2"><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>  <A NAME="soluciones"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Soluciones</div> <div> <B>Soluciones de los ejercicios</B></div> <div> <FONT SIZE="4" COLOR="#006699" FACE="Bell MT" ><B>E</B></FONT>n los ejercicios <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >1</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >6</FONT>, encontrar los primeros cinco términos de la sucesión de las sumas parciales <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >1</FONT>, <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >2</FONT>, <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >3</FONT>, <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >4</FONT><FONT SIZE="1" COLOR="#000000" FACE="Bell MT" > </FONT>y <I>S</I><FONT SIZE="2" COLOR="#000000" FACE="Bell MT" >5</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="2b70e11c0.gif" border=0 width="737" height="284" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="2b868d2d0.gif" border=0 width="653" height="301" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <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="2b88d91b0.gif" border=0 width="473" height="283" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="2b8a8c2c0.gif" border=0 width="396" height="300" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="2b8c63710.gif" border=0 width="611" height="369" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <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="2b8e087f0.gif" border=0 width="776" height="383" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#006699" FACE="Bell MT" ><B>E</B></FONT>n los ejercicios <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >7</FONT> y <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >8</FONT>, determinar si <IMG SRC="2b98651f0.gif" border=0 width="101" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> son convergentes.</div> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="2b9145070.gif" border=0 width="837" height="263" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <IMG SRC="2b9561610.gif" border=0 width="865" height="353" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#006699" FACE="Bell MT" ><B>E</B></FONT>n los ejercicios <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >9</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >18</FONT>, verificar que la serie infinita diverge.</div> <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="2b9601390.gif" border=0 width="769" height="313" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>10</div> <div> <IMG SRC="2b9901390.gif" border=0 width="769" height="313" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <IMG SRC="2b9b01210.gif" border=0 width="769" height="289" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>12</div> <div> <IMG SRC="2b9d01210.gif" border=0 width="769" height="289" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>13</div> <div> <IMG SRC="2b9f501b0.gif" border=0 width="848" height="283" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>14</div> <div> <IMG SRC="2ba2501b0.gif" border=0 width="848" height="283" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>15</div> <div> <IMG SRC="2ba459200.gif" border=0 width="857" height="288" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="16"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>16</div> <div> <IMG SRC="2ba6ac2b0.gif" border=0 width="940" height="299" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>17</div> <div> <IMG SRC="2ba870000.gif" border=0 width="880" height="256" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>18</div> <div> <IMG SRC="2baa50110.gif" border=0 width="848" height="273" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:336px;height:280px" data-ad-client="ca-pub-6266400581769473" data-ad-slot="1163033713"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Acceso rápido a los capítulos del libro "</B><A HREF="id504.htm" TARGET="_top" TITLE="Larson y Edwards"><U><B>Calculo 1 de Larson y Edwards</B></U></A><B>":</B></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>| </B><A HREF="id533.htm" TARGET="_top" TITLE="4.1"><U><B>4.1</B></U></A><B> | </B><A HREF="id505.htm" TARGET="_top" TITLE="4.5"><U><B>4.5</B></U></A><B> | </B><A HREF="id532.htm" TARGET="_top" TITLE="8.5"><U><B>8.5</B></U></A><B> | </B><A HREF="id534.htm" TARGET="_top" TITLE="9.1"><U><B>9.1</B></U></A><B> | </B><A HREF="id542.htm" TARGET="_top" TITLE="9.2"><U><B>9.2</B></U></A><B> |  </B></div> <bR> </td> <td valign="top" 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" VSPACE="0"></B></U></A></div> <div> <B> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="183" BORDERCOLORLIGHT="#006600" BORDERCOLORDARK="#339933" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 374 WIDTH="171"><div> <A HREF="id542_m.htm#definición_de_serie_infinita" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Serie infinita</B></U></A></div> <div> <A HREF="id542_m.htm#definición_de_serie_convergente_y" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Serie convergente y divergente</B></U></A></div> <div> <A HREF="id542_m.htm#serie_telescópica" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Serie telescópica</B></U></A></div> <div> <A HREF="id542_m.htm#serie_geometrica" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Serie geométrica</B></U></A></div> <div> <A HREF="id542_m.htm#propiedades_de_series_infinitas" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Propiedades de series infinitas</B></U></A></div> <div> <A HREF="id542_m.htm#criterio_para_la_divergencia" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Criterio del término n-ésimo para la divergencia</B></U></A></div> <div> <A HREF="id542_m.htm#enunciados" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Enunciados de los ejercicios</B></U></A></div> <div> <A HREF="id542_m.htm#soluciones" TARGET="TRLX_Middle" TITLE="9.2"><U><B><IMG BORDER="0" SRC="Wing0a73007700f000660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Soluciones de los ejercicios</B></U></A></div> <div> <B><IMG BORDER="0" SRC="Wing0a73007700f066660000.gif" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Otros capítulos del libro:</B></div> <DIV ALIGN="LEFT"></DIV> <div> <B>| </B><A HREF="id533.htm" TARGET="_top" TITLE="4.1"><U><B>4.1</B></U></A><B> | </B><A HREF="id505.htm" TARGET="_top" TITLE="4.5"><U><B>4.5</B></U></A><B> | </B><A HREF="id532.htm" TARGET="_top" TITLE="8.5"><U><B>8.5</B></U></A><B> | </B><A HREF="id534.htm" TARGET="_top" TITLE="9.1"><U><B>9.1</B></U></A><B> | </B></div> <div> <B>| </B><A HREF="id542.htm" TARGET="_top" TITLE="9.2"><U><B>9.2</B></U></A><B> | </B></div> </tD> </tR> </TABLE></B></div> <bR> </td> </tr></table></body>