document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=666237>Question 666237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the sum of the first 1000 consecutive whole numbers?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #414348 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=414348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In general, the sum of the first n numbers is  n(n+1)/2.  Then 1000(1000+1)/2 =  500*1001 = 500500.\r<BR>\n" );
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document.write( "If you don't believe the result, here's a nice proof:\r<BR>\n" );
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document.write( "Let S be the sum of the first n numbers.\r<BR>\n" );
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document.write( "S = 1+2+3+...+n \r<BR>\n" );
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document.write( "Also, notice that we can use the commutative property to write S in a different way.\r<BR>\n" );
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document.write( "S = n+n-1+n-2+n-3+...+1\r<BR>\n" );
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document.write( "If we add these two equations we get\r<BR>\n" );
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document.write( "2S = n+1 + n+1 + n+1 +...+ n+1\r<BR>\n" );
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document.write( "How many times do we get n+1?  n times.\r<BR>\n" );
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document.write( "2S = n*(n+1)\r<BR>\n" );
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document.write( "S = n*(n+1)/2  :)\r<BR>\n" );
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document.write( "So, this form will work for any sum 1 to #whatever. </SPAN>\n" );
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