document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144206>Question 1144206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2c. Examine the diagram and explain how it illustrates a value of (n2 + n)/2.\r<BR>\n" );
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document.write( "                                  ⚫⚫⚫🔴<BR>\n" );
document.write( "                                 ⚫⚫🔴🔴    (the sizes of the circles don't matter, just the colors)<BR>\n" );
document.write( "                                 ⚫🔴🔴🔴\r<BR>\n" );
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document.write( "2d. Draw a similar diagram to represent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28n%5E2+%2B+n%29%2F2+ ALIGN=MIDDLE  ALT=\"+%28n%5E2+%2B+n%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for n = 5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765239 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>\r<BR>\n" );
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document.write( "⚫⚫⚫🔴<BR>\n" );
document.write( "⚫⚫🔴🔴<BR>\n" );
document.write( "⚫🔴🔴🔴 \r<BR>\n" );
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document.write( "That diagram illustrates (n^2+n)/2 for n=3.<br><BR>\n" );
document.write( "For n=3, n^2+n = n(n+1) = 3(4); the diagram shows a 3x4 array of circles.  Dividing the array in half diagonally illustrates (n^2+n)/2 for n=3:<br>\r<BR>\n" );
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document.write( "⚫⚫⚫ / 🔴<BR>\n" );
document.write( "⚫⚫ / 🔴🔴<BR>\n" );
document.write( "⚫ / 🔴🔴🔴 \r<BR>\n" );
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document.write( "This array then shows that (n^2+n)/2 for n=3 is equal to 1+2+3 = 6.<br><BR>\n" );
document.write( "For n=5, (n^2+n)/2 = (n(n+1))/2 = (5*6)/2, so the corresponding diagram will show a 5x6 array of circles divided in half diagonally:<br>\r<BR>\n" );
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document.write( "⚫⚫⚫⚫⚫ / 🔴<BR>\n" );
document.write( "⚫⚫⚫⚫ / 🔴🔴<BR>\n" );
document.write( "⚫⚫⚫ / 🔴🔴🔴 <BR>\n" );
document.write( "⚫⚫ / 🔴🔴🔴🔴<BR>\n" );
document.write( "⚫ / 🔴🔴🔴🔴🔴\r<BR>\n" );
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document.write( "And this diagram shows that (n^2+n)/2 for n=5 is equal to 1+2+3+4+5 = 15. </SPAN>\n" );
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