document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761611>Question 761611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum to infinity of a geometric progression is twice the sum of the first two terms. find possible values of the common ratio. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463331 by </B><A HREF=/tutors/aboutme.mpl?userid=ramkikk66><B>ramkikk66(644)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ramkikk66><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=463331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Similar to problem 463319.\r<BR>\n" );
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document.write( "If 'a' is the first term, and 'r' the common ratio of the GP,<BR>\n" );
document.write( "the sum to infinity is given by the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+a+%2F+%281+-+r%29 ALIGN=MIDDLE  ALT=\"S+=+a+%2F+%281+-+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28a+%2B+a%2Ar%29+=+a+%2F+%281-r%29 ALIGN=MIDDLE  ALT=\"2%28a+%2B+a%2Ar%29+=+a+%2F+%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cancelling out a from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%2B+2%2Ar+=+1%2F%281-r%29 ALIGN=MIDDLE  ALT=\"2+%2B+2%2Ar+=+1%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+-+2%2Ar%5E2+=+1 ALIGN=MIDDLE  ALT=\"2+-+2%2Ar%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+1%2F2 ALIGN=MIDDLE  ALT=\"r%5E2+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"r+=+1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"r+=+-1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ":)<BR>\n" );
document.write( " </SPAN>\n" );
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