document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764843>Question 764843</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Gauss's approach to find the following sums(do not use formulas).\r<BR>\n" );
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document.write( "a. 1+2+3+4+...+99<BR>\n" );
document.write( "b. 1+3+5+7+...+97\r<BR>\n" );
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document.write( "a. The sum of the sequence is?<BR>\n" );
document.write( "b. the sum of the sequence is? </SPAN>\n" );
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document.write( "a. 1+2+3+4+...+99\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B99+=+100 ALIGN=MIDDLE  ALT=\"1%2B99+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99%2F2=49.5 ALIGN=MIDDLE  ALT=\"99%2F2=49.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum=100%2A49.5=+4950 ALIGN=MIDDLE  ALT=\"sum=100%2A49.5=+4950\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. 1+3+5+7+...+97\r<BR>\n" );
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document.write( "first find the sum 1+2+3+4+...+97\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B97+=+98 ALIGN=MIDDLE  ALT=\"1%2B97+=+98\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98%2F2=49 ALIGN=MIDDLE  ALT=\"98%2F2=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum=98%2A49=+4802 ALIGN=MIDDLE  ALT=\"sum=98%2A49=+4802\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "since you have only odd numbers, it will be half of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4802 ALIGN=MIDDLE  ALT=\"4802\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2401 ALIGN=MIDDLE  ALT=\"2401\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the sum of 1+3+5+7+...+97 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2401 ALIGN=MIDDLE  ALT=\"2401\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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