document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006529>Question 1006529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1+2+3+...+19)20<BR>\n" );
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document.write( "(21+22+23+...+39)40\r<BR>\n" );
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document.write( "Find 3 (n)s\r<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 #622672 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=622672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "What to find ?\r<BR>\n" );
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document.write( "<U>Comment from student</U>: simplify it into an expression using n<BR>\n" );
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document.write( "OK. (Why do not write it from the very beginning?)\r<BR>\n" );
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document.write( "The sum in the numerator is the sum of first 19 terms of an arithmetic progression 1, 2, 3, . . . , 19\r<BR>\n" );
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document.write( "S = 1 + 2 + 3 + . . . + 19 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+%2B+19%29%2F2%2A19 ALIGN=MIDDLE  ALT=\"%281+%2B+19%29%2F2%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F2%2A19 ALIGN=MIDDLE  ALT=\"20%2F2%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10*19.\r<BR>\n" );
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document.write( "The sum in the numerator is the sum of first 19 terms of an arithmetic progression 21, 22, 23, . . . , 39\r<BR>\n" );
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document.write( "T = 21 + 22 + 23 + . . . + 39 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821+%2B+39%29%2F2%2A19 ALIGN=MIDDLE  ALT=\"%2821+%2B+39%29%2F2%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F2%2A19 ALIGN=MIDDLE  ALT=\"60%2F2%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 30*19.\r<BR>\n" );
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document.write( "Hence, the ratio you are asking for, is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%2A20%29%2F%28R%2A40%29 ALIGN=MIDDLE  ALT=\"%28S%2A20%29%2F%28R%2A40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A19%29%2F%2830%2A19%2A2%29 ALIGN=MIDDLE  ALT=\"%2810%2A19%29%2F%2830%2A19%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%2830%2A2%29 ALIGN=MIDDLE  ALT=\"10%2F%2830%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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