document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175168>Question 175168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An infinite geometric series has 1 and 1/5 as its first two terms: 1, 1/5, 1/25, 1/125,... what is the sum, S, of the infinite series? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130240 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=130240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sequence that generates  1, 1/5, 1/25, 1/125,... is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=%281%2F5%29%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=%281%2F5%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Take note that the sequence is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%2Ar%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%2Ar%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1%2F5 ALIGN=MIDDLE  ALT=\"r=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember, the formula for the sum of an infinite series is\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=a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S=a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=1%2F%281-1%2F5%29 ALIGN=MIDDLE  ALT=\"S=1%2F%281-1%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1%2F5 ALIGN=MIDDLE  ALT=\"r=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=1%2F%284%2F5%29 ALIGN=MIDDLE  ALT=\"S=1%2F%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=5%2F4 ALIGN=MIDDLE  ALT=\"S=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Invert the fraction and multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=5%2F4 ALIGN=MIDDLE  ALT=\"S=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that 1+1/5+1/25+1/125+...=5/4 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );