document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107236>Question 1107236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the value of 9^(1/3) x 9^(1/9) x 9^(1/27) x ...?\r<BR>\n" );
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document.write( "also is there a general formula in solving these types of question? thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722258 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=722258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%5Ex%29%289%5Ey%29%289%5Ez%29=9%5E%28%28x%2By%2Bz%29%29 ALIGN=MIDDLE  ALT=\"%289%5Ex%29%289%5Ey%29%289%5Ez%29=9%5E%28%28x%2By%2Bz%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E%221%2F3%22%2A9%5E%221%2F9%22%2A9%5E%221%2F27%22%2A%22...%22=9%5E%28%28%221%2F3+%2B+1%2F9+%2B+1%2F27+%2B+...%22%29%29=9%5E%221%2F2%22=sqrt%289%29=highlight%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,\r<BR>\n" );
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document.write( "because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3%2B1%2F9%2B1%2F27%2B%22...%22=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F3%2B1%2F9%2B1%2F27%2B%22...%22=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "That sum is the sum of an infinite geometric sequence.<BR>\n" );
document.write( "The \"formula\" for such a sum with a first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a common ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C1 ALIGN=MIDDLE  ALT=\"r%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum=b%2F%281-r%29 ALIGN=MIDDLE  ALT=\"sum=b%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In the case of the sum above, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F3 ALIGN=MIDDLE  ALT=\"b=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1%2F3 ALIGN=MIDDLE  ALT=\"r=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum=%221%2F3%22%2F%281-%221%2F3%22%29=%221%2F3%22%2F%222%2F3%22=1%2F2 ALIGN=MIDDLE  ALT=\"sum=%221%2F3%22%2F%281-%221%2F3%22%29=%221%2F3%22%2F%222%2F3%22=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "There is no need to memorize formulas, if you can deduce them.<BR>\n" );
document.write( "Consider the sum or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=b%2Bbr%2Bbr%5E2%2Bbr%5E3%2B%22...%22%2Bbr%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"S=b%2Bbr%2Bbr%5E2%2Bbr%5E3%2B%22...%22%2Bbr%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rS=br%2Bbr%5E2%2Bbr%5E3%2B%22...%22%2Bbr%5E%28n-1%29%2Bbr%5En ALIGN=MIDDLE  ALT=\"rS=br%2Bbr%5E2%2Bbr%5E3%2B%22...%22%2Bbr%5E%28n-1%29%2Bbr%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rS-S=br%5En-b ALIGN=MIDDLE  ALT=\"rS-S=br%5En-b\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-1%29S=b%28r%5En-1%29 ALIGN=MIDDLE  ALT=\"%28r-1%29S=b%28r%5En-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=b%28r%5En-1%29%2Fr-1 ALIGN=MIDDLE  ALT=\"S=b%28r%5En-1%29%2Fr-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C1 ALIGN=MIDDLE  ALT=\"r%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we might like to write it as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=b%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S=b%281-r%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5En ALIGN=MIDDLE  ALT=\"r%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F%281-r%29 ALIGN=MIDDLE  ALT=\"b%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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