document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117531>Question 1117531</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Does the series converge or diverge? If it converges, what is thr sum? \r<BR>\n" );
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document.write( "E    -4(-1/2)^n-1<BR>\n" );
document.write( "n=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732640 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Step 1:  Plain text notation lesson.  <b>sum[1,infty] -4(-1/2)^(n-1)</b> would be interpreted as \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{n=1}^\infty\,-4\(-\frac{1}{2}\)^{n-1}\">\r<BR>\n" );
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document.write( "2. Convergence:  A geometric series converges if the common ratio <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> is in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -1\ <\ r\ <\ 1\">.  Since  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -1\ <\ -\frac{1}{2} <\ 1\">, this series converges.\r<BR>\n" );
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document.write( "The sum of a convergent geometric series of the form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{n=0}^\infty\ ar^n\ =\ \sum_{n=1}^\infty\ ar^{n-1}\">\r<BR>\n" );
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document.write( "is given by\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{a}{1\ -\ r}\">\r<BR>\n" );
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document.write( "The rest is just arithmetic.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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