document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131912>Question 1131912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write geometric series -9/2+3/2-1/2+1/6- ••• + 1/39366 in summation notation. Using the formula for the sum of an geometric series, compute the sum in the problem above.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748636 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> geometric series -9/2+3/2-1/2+1/6- ••• + 1/39366\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > -the first term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >-the \"common ratio\" between terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > -the nth term\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-9%2F2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%283%2F2%29%2F%28-9%2F2%29 ALIGN=MIDDLE  ALT=\"r=%283%2F2%29%2F%28-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%281%2F1%29%2F%28-3%2F1%29 ALIGN=MIDDLE  ALT=\"r=%281%2F1%29%2F%28-3%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%28-1%2F3%29 ALIGN=MIDDLE  ALT=\"r=%28-1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=-%289%2F2%29%2A%28-1%2F3%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=-%289%2F2%29%2A%28-1%2F3%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sum:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=%28a%5B1%5D%281-r%5En%29%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=%28a%5B1%5D%281-r%5En%29%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=%28-%289%2F2%29%281-%28-1%2F3%29%5En%29%29%2F%281-%28-1%2F3%29%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=%28-%289%2F2%29%281-%28-1%2F3%29%5En%29%29%2F%281-%28-1%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use  last given term  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F39366 ALIGN=MIDDLE  ALT=\"1%2F39366\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plug it in\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=-%289%2F2%29%2A%28-1%2F3%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=-%289%2F2%29%2A%28-1%2F3%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...last given term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F39366 ALIGN=MIDDLE  ALT=\"1%2F39366\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F39366=-%289%2F2%29%2A%28-1%2F3%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"1%2F39366=-%289%2F2%29%2A%28-1%2F3%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F39366%29%2F%28-9%2F2%29=%28-1%2F3%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"%281%2F39366%29%2F%28-9%2F2%29=%28-1%2F3%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F177147=%28-1%2F3%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"-1%2F177147=%28-1%2F3%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...take log of both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-log%281%2F177147%29=-log%28%281%2F3%29%5E%28n-1%29%29 ALIGN=MIDDLE  ALT=\"-log%281%2F177147%29=-log%28%281%2F3%29%5E%28n-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-log%281%2F177147%29=-%28n-1%29log%28%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"-log%281%2F177147%29=-%28n-1%29log%28%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1=%28-log%281%2F177147%29%29%2F%28-log%28%281%2F3%29%29%29 ALIGN=MIDDLE  ALT=\"n-1=%28-log%281%2F177147%29%29%2F%28-log%28%281%2F3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1=log%281%2F177147%29%2Flog%28%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"n-1=log%281%2F177147%29%2Flog%28%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1=11 ALIGN=MIDDLE  ALT=\"n-1=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=11%2B1 ALIGN=MIDDLE  ALT=\"n=11%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=12 ALIGN=MIDDLE  ALT=\"n=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=>\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D=%28-%289%2F2%29%281-%28-1%2F3%29%5E12%29%29%2F%281%2B1%2F3%29 ALIGN=MIDDLE  ALT=\"S%5B12%5D=%28-%289%2F2%29%281-%28-1%2F3%29%5E12%29%29%2F%281%2B1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D=%28-%289%2F2%29%281-1%2F531441%29%29%2F%284%2F3%29 ALIGN=MIDDLE  ALT=\"S%5B12%5D=%28-%289%2F2%29%281-1%2F531441%29%29%2F%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D=%28-%289%2F2%29%28531440%2F531441%29%29%2F%284%2F3%29 ALIGN=MIDDLE  ALT=\"S%5B12%5D=%28-%289%2F2%29%28531440%2F531441%29%29%2F%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D=%28-265720%2F59049%29%2F%284%2F3%29 ALIGN=MIDDLE  ALT=\"S%5B12%5D=%28-265720%2F59049%29%2F%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D=-66430%2F19683 ALIGN=MIDDLE  ALT=\"S%5B12%5D=-66430%2F19683\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D=-3 ALIGN=MIDDLE  ALT=\"S%5B12%5D=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7381%2F19683 ALIGN=MIDDLE  ALT=\"+7381%2F19683\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );