document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703760>Question 703760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need help to find the sum of the first 500 integers.<BR>\n" );
document.write( "I know that the answer is 125,500 and that I need to add 500 to 1, 499+2, 498+3, 497+4, 496+5...and then to multiply by 250 (500/2), but how to put it into a formula that works for all numbers in the row, so that the sum is always 125,500?<BR>\n" );
document.write( "The formula S=n(n+1)/2 works only for 500: S=500(500+1)/2=125,500, BUT<BR>\n" );
document.write( "if S=499 (499+1)/2, it doesn't work.<BR>\n" );
document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433719 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=433719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Try the formula carefully to see that it works for both values.\r<BR>\n" );
document.write( "\n" );
document.write( "n=499,<BR>\n" );
document.write( "S=499(499+1)/2<BR>\n" );
document.write( "=499(500)/2<BR>\n" );
document.write( "=499(250)<BR>\n" );
document.write( "=124750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n=500,<BR>\n" );
document.write( "S=500(500+1)/2<BR>\n" );
document.write( "=250(501)<BR>\n" );
document.write( "=125250\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Difference is 125250-124750=500.<BR>\n" );
document.write( "The formula works for both values of n. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );