document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888258>Question 888258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sum the Series:<BR>\n" );
document.write( "1×2+2×3+3×4+4×5+&#8943;+2013×2014<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537264 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=537264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a quadratic series whose members are given as<BR>\n" );
document.write( "     2   6   12   20   30 ......4054182<BR>\n" );
document.write( "     1   2    3    4    5        2013<BR>\n" );
document.write( "n^2  1   4    9   16   25       4052169<BR>\n" );
document.write( "a member in the geometric sequence is given by<BR>\n" );
document.write( "nth term = n^2 +n<BR>\n" );
document.write( "now we know that the summation of n^2 = n[n+1][2n+1]/6 and<BR>\n" );
document.write( "summation of n is n(n+1)/2<BR>\n" );
document.write( "therefore the sum(S) of the series is<BR>\n" );
document.write( "S = 2013(2014)(2*2013+1)/6 + 2013(2014)/2<BR>\n" );
document.write( "S = 16326190914/6 + 4054182/2<BR>\n" );
document.write( "S = 2721031819 +  2027091<BR>\n" );
document.write( "S = 2723058910<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );