document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41021>Question 41021</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?<BR>\n" );
document.write( "a)1/25<BR>\n" );
document.write( "b)1/4<BR>\n" );
document.write( "c)1<BR>\n" );
document.write( "d)5/4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26488 by </B><A HREF=/tutors/aboutme.mpl?userid=mszlmb><B>mszlmb(115)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mszlmb><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=mszlmb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I LOVE infinite series.<BR>\n" );
document.write( "ok so 1+1/5+1/25+1/125+1/625...<BR>\n" );
document.write( "1+.2+.04+.008+.0016<BR>\n" );
document.write( "or 1+(1*2)/10+(1*4)/100+(1*8)/1000...<BR>\n" );
document.write( "or 1+...<BR>\n" );
document.write( "we have 1/5+1/25=6/25+1/125=31/125+1/625=156/625 and so on<BR>\n" );
document.write( "so y=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28%28%281%2A5%2B1%29%2A5%2B1%29%2A5%2B1%29%2A5%2B1%29%2A5%2B1%29 ALIGN=MIDDLE  ALT=\"%28%28%28%28%281%2A5%2B1%29%2A5%2B1%29%2A5%2B1%29%2A5%2B1%29%2A5%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or, ignoring the order of whatever its called,<BR>\n" );
document.write( "we add one and multiply by 5 over and over again, infinitely, over<BR>\n" );
document.write( "0+1*5+1*5+1*5...<BR>\n" );
document.write( "_____________<BR>\n" );
document.write( "5(5)(5)(5)(5)<BR>\n" );
document.write( "yielding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28%28%280%2B1%295%2B1%295%2B1%295%2B1%295%2B1%295...%29%2F5%2A5%2A5%2A5%2A5... ALIGN=MIDDLE  ALT=\"%28%28%28%28%280%2B1%295%2B1%295%2B1%295%2B1%295%2B1%295...%29%2F5%2A5%2A5%2A5%2A5...\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%280%2B1%29%2F5%29%2A%28125%2F6%29 ALIGN=MIDDLE  ALT=\"%28%280%2B1%29%2F5%29%2A%28125%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ok forget all of that, a lot of it is wrong.  But be ready to refer to it.  don't worry if it made no sense.\r<BR>\n" );
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document.write( "now im very sorry, i feel quite childish in terms of intellect; perhaps you can solve it from here..<BR>\n" );
document.write( "I got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28x%2F5%5Ex%29 ALIGN=MIDDLE  ALT=\"E%28x%2F5%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...:P I can't solve it anymore!\r<BR>\n" );
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document.write( "I do, however, feel like much less of a mathematical amateur telling you that the answer is obviously, of the four choices listed above, 5/4, because its the only number higher than one, and seeing as how this infinite series is 1+ something.. well, you can make the connection:)\r<BR>\n" );
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document.write( "I would REALLY appreciate it if you could perhaps teach me by way of email how to get the solution when you do\r<BR>\n" );
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document.write( "yours truly, <-)))><mszlmb><(((-><BR>\n" );
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document.write( "<b>sorry about all that, i worked on it today..here's what iv come up with..</b><BR>\n" );
document.write( "<center>so we have 1+.2+.04+.008 etc.<br>Do you see the pattern, again, of *2 and *5?</center><BR>\n" );
document.write( "<center>This can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex%2F10%5Ex ALIGN=MIDDLE  ALT=\"2%5Ex%2F10%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That's to get any the xth number (ie the 5th number is 32/100000, or .000032; try it.)</center><BR>\n" );
document.write( "<center>Of course, this is not what we want, we want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%5BN%5Dx ALIGN=MIDDLE  ALT=\"E%5BN%5Dx\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%5Ex%2F10%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29=2%5Ex%2F10%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >; E, representing sigma, means the addition of all of the following.  By E[N] I mean sigma of all N, positive integers.  (E[n]{1,2,3.4,5}=8)<BR>\n" );
document.write( "we're basically looking for all solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex%2F10%5Ex ALIGN=MIDDLE  ALT=\"2%5Ex%2F10%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > given x=N (positive integer).<BR>\n" );
document.write( "this can also be expressed as E[n]<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5Ex%2F5%5Ex ALIGN=MIDDLE  ALT=\"1%5Ex%2F5%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >; I can simplify it no further as of now.\r<BR>\n" );
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document.write( "Again, it is obvious the answer is 5/4 because it is the only choice over 1, an easy choice considering the question is 1+something.<BR>\n" );
document.write( "I checked, and it really does equal 5/4; I just can't find how to get there :P<BR>\n" );
document.write( "good luck and if u get the process email me ;) </SPAN>\n" );
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