document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112554>Question 1112554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sum of infinite gp is 2 and sum of their cubes of the terms is 8/7 find gp </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727621 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first equation needed is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sum%28a%2Ar%5En%2C+0%2C+infinity%29+=++a%2F%281-r%29+ ALIGN=MIDDLE  ALT=\"+sum%28a%2Ar%5En%2C+0%2C+infinity%29+=++a%2F%281-r%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = 2    \r<BR>\n" );
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document.write( "The 2nd equation may not be as obvious but if you substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A=a%5E3+ ALIGN=MIDDLE  ALT=\"+A=a%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=r%5E3 ALIGN=MIDDLE  ALT=\"R=r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the infinite sum formula for a GP, you will find:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sum%28a%5E3%2Ar%5E%283n%29%2C+0%2C+infinity%29+=+a%5E3%2F%281-r%5E3%29+ ALIGN=MIDDLE  ALT=\"+sum%28a%5E3%2Ar%5E%283n%29%2C+0%2C+infinity%29+=+a%5E3%2F%281-r%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8/7     \r<BR>\n" );
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document.write( "These two equations can be solved for  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28a=1%29+ ALIGN=MIDDLE  ALT=\"+highlight%28a=1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+r=1%2F2+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+r=1%2F2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "———————————\r<BR>\n" );
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document.write( "The work-out:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2F%281-r%29+=+2+ ALIGN=MIDDLE  ALT=\"+a%2F%281-r%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  —>   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2-2r+ ALIGN=MIDDLE  ALT=\"+a+=+2-2r+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E3%2F%281-r%5E3%29+=+8%2F7+ ALIGN=MIDDLE  ALT=\"+a%5E3%2F%281-r%5E3%29+=+8%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > —>   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E3+=+%288%2F7%29%281-r%5E3%29+ ALIGN=MIDDLE  ALT=\"+a%5E3+=+%288%2F7%29%281-r%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282-2r%29%5E3++=+%288%2F7%29%281-r%5E3%29+ ALIGN=MIDDLE  ALT=\"+%282-2r%29%5E3++=+%288%2F7%29%281-r%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   …. after some algebra ...<BR>\n" );
document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-6r%5E3+%2B21r%5E2+-+21r+%2B+6+=+0+ ALIGN=MIDDLE  ALT=\"++-6r%5E3+%2B21r%5E2+-+21r+%2B+6+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This has solutions  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r=1%2F2+ ALIGN=MIDDLE  ALT=\"+r=1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r=1+ ALIGN=MIDDLE  ALT=\"+r=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r=2+ ALIGN=MIDDLE  ALT=\"+r=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r=1%2F2+ ALIGN=MIDDLE  ALT=\"+r=1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > maintains  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28r%29+%3C+1+ ALIGN=MIDDLE  ALT=\"+abs%28r%29+%3C+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (as required for convergence of infinite GP)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2-2r+=+2-2%281%2F2%29+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+2-2r+=+2-2%281%2F2%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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