document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096429>Question 1096429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> evaluate 1+3^2+3^3+..++..3^60 everything divided by 3^61-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710961 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>The expression as you show it is<br><BR>\n" );
document.write( "(1+3^2+3^3+...+3^60)/(3^61-1)<br><BR>\n" );
document.write( "I suspect you have omitted one term from the numerator, so that the expression is supposed to be<br><BR>\n" );
document.write( "(1+3+3^2+3^3+...+3^60)/(3^61-1)<br><BR>\n" );
document.write( "If that is indeed what the expression is supposed to be then the formula for the sum of a finite geometric series tells us that the numerator is equivalent to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E61-1%29%2F%283-1%29+=+%283%5E61-1%29%2F2 ALIGN=MIDDLE  ALT=\"%283%5E61-1%29%2F%283-1%29+=+%283%5E61-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and so the entire expression is equal to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%5E61-1%29%2F2%29%2F%283%5E61-1%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%28%283%5E61-1%29%2F2%29%2F%283%5E61-1%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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