document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=601352>Question 601352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a nice simple formula for finding what sum is for ANY value n.  Explain why it works.\r<BR>\n" );
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document.write( "2+4+6+8+...+2n=?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379876 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=379876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2+4+6+...+2n = n(n+1). You can prove it by induction. Or you can use the \"Gauss-style\" method of adding that expression to itself, i.e.\r<BR>\n" );
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document.write( "S = 2 + 4 + 6 +...+ 2n<BR>\n" );
document.write( "S = 2n+ ...       + 2<BR>\n" );
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document.write( "2S = (2n+2) + (2n+2) + ... + (2n+2) = (2n+2)(n)\r<BR>\n" );
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document.write( "S = n(n+1) </SPAN>\n" );
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