document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=483711>Question 483711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you evaluate an infinite geometric series? <BR>\n" );
document.write( "ex: 1.1+0.11+0.011+.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331016 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20855)</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=331016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "In a geometric series, finite or infinite, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=common ALIGN=MIDDLE  ALT=\"common\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ratio ALIGN=MIDDLE  ALT=\"ratio\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the multiplier used to get each succeeding term.  Or, you can think of it as any term divided by the previous one.  \r<BR>\n" );
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document.write( "For example, in the series you have\r<BR>\n" );
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document.write( "1.1+0.11+0.011+.............the common ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1 ALIGN=MIDDLE  ALT=\"0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "If an infinite geometric series has a ratio whose absolute value is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and so has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum ALIGN=MIDDLE  ALT=\"sum\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the formula is\r<BR>\n" );
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document.write( "             <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28inf%29+=+a+%2F+%281-r%29 ALIGN=MIDDLE  ALT=\"S%28inf%29+=+a+%2F+%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( " where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28inf%29 ALIGN=MIDDLE  ALT=\"S%28inf%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > just stands for the sum of an infinite series,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a ALIGN=MIDDLE  ALT=\"+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the first term, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the common ratio.\r<BR>\n" );
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document.write( "in your case:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28inf%29+=+1.1+%2F+%281-0.1%29 ALIGN=MIDDLE  ALT=\"S%28inf%29+=+1.1+%2F+%281-0.1%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=S%28inf%29+=+1.1+%2F+%280.9%29 ALIGN=MIDDLE  ALT=\"S%28inf%29+=+1.1+%2F+%280.9%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=S%28inf%29+=+1.2222222222222222222222222222222 ALIGN=MIDDLE  ALT=\"S%28inf%29+=+1.2222222222222222222222222222222\"   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=S%28inf%29+=+1.2 ALIGN=MIDDLE  ALT=\"S%28inf%29+=+1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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