document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084210>Question 1084210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the sum:\r<BR>\n" );
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document.write( "4/sigma/n=1 (2/3)^n-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698282 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=698282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\"><BR>\n" );
document.write( "I'm assuming the summation you want to do is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{n = 1}^{4}\left(\frac{2}{3}\right)^{n-1}\">\r<BR>\n" );
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document.write( "If n = 1, then (2/3)^(n-1) = (2/3)^(1-1) = (2/3)^0 = 1<BR>\n" );
document.write( "If n = 2, then (2/3)^(n-1) = (2/3)^(2-1) = (2/3)^1 = 2/3<BR>\n" );
document.write( "If n = 3, then (2/3)^(n-1) = (2/3)^(3-1) = (2/3)^2 = 4/9<BR>\n" );
document.write( "If n = 4, then (2/3)^(n-1) = (2/3)^(4-1) = (2/3)^3 = 8/27\r<BR>\n" );
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document.write( "Therefore, summing from n = 1 to n = 4 yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{n = 1}^{4}\left(\frac{2}{3}\right)^{n-1} \ \  = (1)+(2/3)+(4/9)+(8/27)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{n = 1}^{4}\left(\frac{2}{3}\right)^{n-1} \ \   = (27/27)+(18/27)+(12/27)+(8/27)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{n = 1}^{4}\left(\frac{2}{3}\right)^{n-1} \ \   = (27+18+12+8)/27\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{n = 1}^{4}\left(\frac{2}{3}\right)^{n-1} \ \   = 65/27\">\r<BR>\n" );
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document.write( "The answer would be the fraction 65/27.\r<BR>\n" );
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