document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=447576>Question 447576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the sum of the first 500 counting numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308100 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=308100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "500 + 1 = 501\r<BR>\n" );
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document.write( "499 + 2 = 501\r<BR>\n" );
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document.write( "498 + 3 = 501\r<BR>\n" );
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document.write( ". . .\r<BR>\n" );
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document.write( "251 + 250 = 501\r<BR>\n" );
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document.write( "And there are 500/2 = 250 such pairs.\r<BR>\n" );
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document.write( "In general, the sum of consecutive positive integers is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i\,=\,a}^l\,(i)\ =\ \frac{(a\,+\,l)(l\,-\,a\,+\,1)}{2}\">\r<BR>\n" );
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document.write( "So for your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i\,=\,1}^{500}\,(i)\ =\ \frac{(1\,+\,500)(500\,-\,1\,+\,1)}{2}\ =\ 501\ \times\ 250\">\r<BR>\n" );
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document.write( "Super Double Plus Extra Credit:\r<BR>\n" );
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document.write( "What is the sum of the <i><b>even</b></i> integers between 200 and 300 inclusive?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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