document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278912>Question 278912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of the first 100 odd numbers minus the sum of the first 100 numbers<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 #202871 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=202871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The sum of the first 100 odd numbers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^{100}\,{2i\ -\ 1}\">\r<BR>\n" );
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document.write( "The sum of the first 100 numbers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^{100}\,{i}\">\r<BR>\n" );
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document.write( "The first 100 odd minus the first 100\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^{100}\,\left(2i\ -\ 1\right)\ -\ \sum_{i=1}^{100}\,\left(i\right)\ =\ \sum_{i=1}^{100}\,\left(2i\ -\ 1\right)\ -\ \left(i\right)\ = \ \sum_{i=1}^{100}\,\left(i\ -\ 1\right)\">\r<BR>\n" );
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document.write( "The first term of the resulting series (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 1\">) is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1\ -\ 1\ =\ 0\">\r<BR>\n" );
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document.write( "The last term of the resulting series (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 100\">) is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 100\ -\ 1\ =\ 99\">\r<BR>\n" );
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document.write( "And there are still <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 50\"> terms, so the sum is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(a\ +\ l\right)\left(n\right)}{2}\ =\ \frac{(0\ +\ 99)(100)}{2}\ =\ 99\,\cdot\,50\ =\ 4950\">\r<BR>\n" );
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document.write( "Verification that  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^{100}\,{2i\ -\ 1}\ =\ 10,000\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^{100}\,{i}\ =\ 5050\">\r<BR>\n" );
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document.write( "and therefore\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^{100}\,\left(2i\ -\ 1\right)\ -\ \sum_{i=1}^{100}(i)\ =\ 10000\ -\ 5050\ =\ 4950\">\r<BR>\n" );
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document.write( "is left as an exercise for the student.\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" );
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