document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=504502>Question 504502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IF x=1+3+3^2+3^3+3^4+3^5+3^6+3^7+3^8+3^9+3^10<BR>\n" );
document.write( "then y=3x+1<BR>\n" );
document.write( "What is the value of x-y? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339624 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (I'll use sigma notation to make it more compact)\r<BR>\n" );
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document.write( "If\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \sum_{i=0}^{10} 3^i\">, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3x = \sum_{i=1}^{11} 3^i\">, and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y = 1+\sum_{i=1}^{11} 3^i\">\r<BR>\n" );
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document.write( "Therefore,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y - x = (1+\sum_{i=1}^{11} 3^i) - \sum_{i=0}^{10} 3^i\">\r<BR>\n" );
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document.write( "The 3^1, 3^2, ..., 3^10 will cancel, leaving\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y-x = (1 + 3^{11}) - 3^0 = 3^{11}\"> as our answer. </SPAN>\n" );
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